I 


"I  '•' 

i 

t 


IN  MEMORIAM 
FLOR1AN  CAJORI 


PRACTICAL  BUSINESS 
ARITHMETIC 


BY 

JOHN  H.  MOORE 

COMMERCIAL  DEPARTMENT,  CHARLESTOWN  HIGH  SCHOOL,  BOSTON 
AND 

GEORGE  W.  MINER 

COMMERCIAL  DEPARTMENT,  WESTFIELP  (MASS.)  HIGH  SCHOOL 


GINN  &  COMPANY 

BOSTON  -  NEW  YORK  •  CHICAGO  •  LONDON 


COPYRIGHT,  1906,  BY 
JOHN  H.  MOORE  AND  GEORGE  W.  MIXER 


ALL  RIGHTS   RESERVED 


(Cftc  gtftenaum 

GINN  &  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


PREFACE 

THIS  work  has  been  prepared  with  the  belief  that  it  will  be 
of  genuine  service  to  all  interested  in  business  education.  It 
is  particularly  planned  for  students  pursuing  a  commercial 
course  in  business  schools,  high  schools,  and  normal  schools. 

The  constant  aim  of  the  authors  has  been  to  develop  the 
subject  in  such  a  way  as  to  make  it  possible  for  the  student  to 
realize  both  the  utilitarian  and  the  cultural  value  of  arithmetic. 
The  topics  have  been  selected  with  great  care,  and  a  logical 
unfolding  of  the  whole  subject  has  been  kept  in  view.  An 
attempt  has  been  made  to  give  problems  which  appeal  to  the 
needs  and  interests  of  the  business  student,  and  so  to  grade  and 
group  these  problems  as  to  make  the  mind-furnishing  and  mind- 
developing  qualities  of  the  subject  go  hand  in  hand.  Inherited 
puzzles  and  manufactured  conditions  which  give  a  false  notion 
of  business  have  been  studiously  avoided.  The  subject  as  a 
whole  has  been  modernized,  and  the  exercises  made  simple, 
natural,  and  straightforward. 

The  most  important  part  of  the  arithmetic,  considered  from 
a  business  standpoint,  is  that  part  devoted  to  the  four  funda- 
mental'processes  and  fractions.  Particular  attention  has  there- 
fore been  devoted  to  the  chapters  in  this  part  of  the  book.  The 
need  for  speed  and  accuracy  is  emphasized  in  many  different 
ways.  There  are  many  speed  exercises,  and  the  student  is 
taught  to  check  his  work  at  every  step.  To  make  the  work 
more  real,  many  self-checking  problems,  taken  from  actual 
business  transactions,  are  given. 

Many  classes  in  high  schools  study  business  arithmetic  before 
they  have  taken  up  the  subject  of  bookkeeping.  To  bring  all 

Hi 


iv  PREFACE 

the  work  of  the  text  within  the  understanding  of  such  classes, 
the  principles  of  debit  and  credit  and  of  simple  account-keeping 
are  developed  in  the  chapter  on  subtraction. 

The  method  of  introducing  all  new  topics  is  inductive  rather 
than  deductive.  The  student  is  led  to  discover  as  much  as 
possible  for  himself.  Useless  lists  of  so-called  "principles" 
and  all  worthless  definitions  have  been  omitted ;  but  principles 
which  portray  business  customs  and  definitions  which  are 
understandable  and  valuable  have  been  carefully  stated.  No 
arbitrary  rules  are  given.  When  a  rule  is  thought  necessary 
to  promote  facility  and  rapidity  in  numerical  calculation,  the 
student  is  induced  to  make  it  for  himself. 

Many  new  topics  have  been  added,  and  many  of  the  obsolete 
topics  which  have  so  long  encumbered  the  arithmetics  of  the 
schools  have  been  eliminated.  The  simple  exercises  on  graphic 
methods  of  representing  statistics,  the  exercises  on  plotting  and 
on  reading  scales,  and  the  exercises  on  calculation  tables,  tariffs, 
freight  and  express  schedules,  price  lists,  stock  and  bond  quo- 
tations, etc.,  will,  it  is  believed,  be  welcomed  by  progressive 
teachers.  On  the  other  hand,  the  elimination  of  cube  root  and 
its  applications,  compound  proportion  and  compound  partner- 
ship, unreal  fractions  of  all  kinds,  all  of  the  useless  matter  com- 
monly given  under  denominate  numbers,  present  worth  and 
true  discount,  and  various  other  obsolete  topics,  will  add  to  the 
effectiveness  of  the  course. 

Many  students  who  can  solve  the  difficult  problems  of  a  text- 
book often  fail  in  the  solution  of  the  ordinary  problems  of 
business.  One  reason  for  this  is  that  the  problems  of  business 
are  never  labeled  according  to  the  case  or  the  principles  in- 
volved in  their  solution.  Recognizing  this,  the  authors  have 
avoided  the  usual  division  of  the  topics  into  cases.  General 
principles  are  developed  and  applied  through  groups  of  related 
problems.  These  problems  enable  the  student  to  view  a  ques- 
tion from  all  sides  and  to  acquire  a  knowledge  of  current  busi- 
ness methods  as  well  as  skill  in  numerical  calculation. 

To  make  the  problems  vivid  and  lifelike  numerous  photo- 


PREFACE  V 

graphs  of  actual  business  papers  have  been  reproduced.  These 
facsimiles  serve  two  good  and  useful  purposes,  —  one,  to  place 
the  problems  before  the  student  just  as  they  will  come  to  him 
in  real  business  ;  the  other,  to  give  him  that  familiarity  with 
common  business  forms  which  of  itself  is  an  invaluable  part  of 
any  training  in  business  arithmetic.  Pictures  and  diagrams 
have  been  freely  used  whenever  they  seemed  likely  to  throw 
light  on  either  principles  or  problems. 

The  abundance  of  oral  work  given  in  connection  with  every 
chapter  will,  it  is  thought,  add  to  the  value  of  the  book. 
These  exercises  are  used  to  illustrate  new  principles,  to  prepare 
the  student  for  written  work,  to  introduce  and  develop  short 
processes,  to  cultivate  rapidity  and  accuracy  in  calculation,  and 
to  teach  close  and  accurate  thinking.  Such  oral  work  as  is 
given  is  an  absolute  business  requirement  and  a  tool  for  proper 
training  in  analysis  and  expression. 

The  authors  wish  to  acknowledge  their  indebtedness  to 
Dr.  David  Eugene  Smith,  Professor  of  Mathematics,  Teachers 
College,  Columbia  University,  New  York,  who  read  the  com- 
plete manuscript  and  much  of  the  proof,  and  kindly  made 
numerous  suggestions  for  the  betterment  of  the  book ;  to  Mr. 
George  M.  Clough  for  the  larger  part  of  the  material  in  the 
chapter  on  life  insurance ;  to  Mr.  George  Abbot  of  Brown 
Bros.  &  Co.,  Boston,  and  to  Mr.  H.  T.  Smith,  Assistant  Cashier 
of  the  Shawmut  National  Bank,  Boston,  for  valuable  assistance 
on  the  chapters  on  interest  and  banking. 


CONTENTS 

FUNDAMENTAL   PROCESSES 

CHAPTER  PAGE 

I.     INTRODUCTION 1 

II.     NOTATION  AND  NUMERATION 2 

III.  UNITED  STATES  MONEY 8 

IV.  ADDITION  .         .         .         .         .         .         .         .        .        .        .10 

V.     SUBTRACTION 31 

VI.     MULTIPLICATION       .........  50 

VII.     DIVISION 64 

VIII.     AVERAGE .  79 

IX.     CHECKING  RESULTS 81 

FRACTIONS 

X.     DECIMAL  FRACTIONS 85 

XI.     FACTORS,  DIVISORS,  AND  MULTIPLES 107 

XII.     COMMON  FRACTIONS 113 

XIII.  ALIQUOT  PARTS 150 

XIV.  BILLS  AND  ACCOUNTS 160 

DENOMINATE   NUMBERS 

XV.     DENOMINATE  QUANTITIES 181 

XVI.     PRACTICAL  MEASUREMENTS 193 

PERCENTAGE   AND  ITS   APPLICATIONS 

XVII.    PERCENTAGE 227 

XVIII.     COMMERCIAL  DISCOUNTS 242 

XIX.     GAIN  AND  Loss 252 

XX.    MARKING  GOODS      .        . 260 

XXI.     COMMISSION  AND  BROKERAGE 266 

vii 


Vlll 


CONTENTS 


CHAPTER 

XXII.  PROPERTY  INSURANCE 

XXIII.  STATE  AND  LOCAL  TAXES 

XXIV.  CUSTOMS  DUTIES 


PAGE 

273 

280 
285 


INTEREST   AND   BANKING 

XXV.  INTEREST 

XXVI.  BANK  DISCOUNT 

XXVII.  PARTIAL  PAYMENTS 

XXVIII.  BANKERS'  DAILY  BALANCES     . 

XXIX.  SAVINGS-BANK  ACCOUNTS 

XXX.  EXCHANGE 

EQUATIONS   AND  CASH    BALANCE 

XXXI.    EQUATION  OF  ACCOUNTS  .... 
XXXII.     CASH  BALANCE 

DIVIDENDS   AND   INVESTMENTS 

XXXIII.  STOCKS  AND  BONDS 

XXXIV.  LIFE  INSURANCE 


294 
320 
332 
340 
343 
346 


376 
385 


388 
410 


PARTITIVE   PROPORTION,   PARTNERSHIP,    AND   STORAGE 

XXXV.    PARTITIVE  PROPORTION  AND  PARTNERSHIP    .        .        .     416 
XXXVI.     STORAGE 433 

APPENDIX 439 

TABLES  OF  MEASURES 439 

ABBREVIATIONS  AND  SYMBOLS  .  442 


INDEX    ....  443 


PRACTICAL  BUSINESS  ARITHMETIC 

FUNDAMENTAL   PROCESSES 
CHAPTER  I 

INTRODUCTION 

1.  It  is  assumed  at  the  outset  that  the  student  is  familiar 
with  the  ordinary  symbols  of  operation ;  that  he  can  read  and 
write  numbers  ;  that  he  can  add,  subtract,  multiply,  and  divide 
integers ;  that  he  can  do  simple  work  in  United  States  money 
and  in   common   and   decimal   fractions ;    and   that  he   knows 
many  of  the  most  common  uses  of  arithmetic. 

2.  In  this  course  in  business  arithmetic  he  may  learn  more 
about  methods  of  working  with  numbers ;  the  uses  of  arithmetic 
in  the  most  important  lines  of  business  and  in  the  ordinary 
affairs   of   everyday  life ;    how  to   acquire   skill   in    handling 
numbers ;  how  to  check  results ;    and  how  to  make  problems 
and  solve  them.     Besides  all  this,  he  may  learn  a  great  deal 
about    system  and   economy  in  the  home  and   in  the    office ; 
current  business  practices  and  usages ;    business  phraseology 
and  literature ;   the  quantitative  side  of  commerce  and  indus- 
try ;  and  many  other  useful  arid  interesting  items  of  informa- 
tion pertaining  to  his  active  participation  in  life. 

3.  The  fundamental  processes  are  the  foundation  of  all  arith- 
metic.    The  student  should  therefore  be  able  to  perform  these 
essential  processes  with  speed,  absolute  accuracy,  and  intelligence 
before  he  attempts  to  take  up  the  more  advanced  work. 

Where  work  in  the  fundamental  processes  is  not  thought  to  be  advisable 
it  may  of  course  be  omitted. 

1 


CHAPTER   II 

NOTATION  AND  NUMERATION 
ORAL  EXERCISE 

1.  How  many  different  figures  are  used  to  express  numbers  ? 

2.  What  is  the  meaning  of  the  syllable  teen  in  the  numbers 
from  13  to  19  inclusive  ? 

3.  What  is  the  meaning  of  the  syllable  ty  in  such  numbers 
as  20,  30,  40,  45,  75,  87,  96  ? 

4.  What  name  is  given  to  10  tens?  to  10  hundreds?  to  1000 
thousands?  to  1000  millions? 

5.  In  7,  70,  700,  7,000,  and  70,000  how  does  the  7  change  in 
value  ?    In  7007  how  do  the  values  of  the  7's  compare? 

6.  What  is  the  value  of  the  cipher  in  any  number  ?    Why  is 
it  used  ?     Explain  the  use  of  the  ciphers  in  900,905. 

7.  Upon  what  two  things  does  the  value  of  a  figure  depend  ? 
Illustrate  your  answer,  using  the  number  121,000,121. 

8.  Mention  five  things  that  are  counted  in  thousands ;  three 
things  that  are  counted  in  millions  ;  two  things  that  are  counted 
in  billions.      Can  you  think  of  any  use  for  trillions  ? 

9.  Read  aloud  the  following  : 

a.  The  coinage  of  the  mints  at  Philadelphia,  New  Orleans, 
and  San  Francisco  during  a  recent  year  amounted  to  176,999,132 
pieces,  of  a  value  of  $136,340,781.     Of  this  199,065,715  was  in 
gold  coin,  124,298,850   in  silver  dollars,  and  $12,976,216  in 
fractional  silver  and  minor  coins. 

b.  In  the  United  States  Bureau  of  Engraving  and  Printing 
there  are    printed    yearly  about    20,000,000  sheets  of    United 
States  notes,  certificates  of  deposit,  bonds,  and  national  currency 
to  the  amount  of  about  1500,000,000.    In  addition  to  this  there 
are  printed  about  1,000,000,000  internal  revenue  stamps,  and 
more  than  3,000,000,000  postage  stamps. 

2 


NOTATION   AND   NUMERATION 


THE   ARABIC   SYSTEM 

4.  This  is  the  common  system  of  notation.     It  is  generally 
called  the  Arabic  system  because  the  numerals  which  it  employs 
were  introduced  into  Europe  by  the  Arabs. 

The  Arabic  numerals  1,2,  3,  and  so  on  to  9  originated  in  India  about  2000 
years  ago.  When  only  these  numerals  were  used,  the  system  proved  to  be  cum- 
bersome, and  all  mathematical  operations  involved  great  difficulty.  About 
1200  years  ago  the  cipher  0  was  added,  thus  making  a  system  sufficiently 
ample  and  simple  for  ordinary  purposes  of  analysis  and  investigation.  The 
Arabs  introduced  the  system  into  Europe  in  the  twelfth  century,  but  it  was 
not  until  about  300  years  later  that  it  displaced  the  clumsy  Roman  system. 

5.  The    distinctive    feature   of    the   Arabic    system    is   the 
place  value  of  the  numerals  employed.     The  value  of  an  Arabic 
numeral  depends  as  much  upon  its  place  in  the  number  as 
upon  its  simple  or  digit  value. 

Thus,  in  the  Roman  system,  VII  =  5  +  1  +  1.  In  the  Arabic  system, 
511  =  5  hundreds  +  1  ten  +  1.  5  has  not  only  the  unit  value  Jive,  but  also 
the  place  value  hundreds;  and  the  1  following  has  not  only  the  unit  value 
one,  but  also  the  place  value  ten. 

6.  The  successive  places  a  figure  may  occupy  in  a  number 
are  called  orders  of  units. 

7.  Orders    of  units  increase  from  right  to  left  and   decrease 
from  left  to  right  in  a  tenfold  ratio.     Therefore, 

8.  The    Arabic    system    of    notation    is    properly   called   a 
decimal  system,  from  the  Latin  decem,  meaning  ten. 

9.  A  comma  (separatrix)  or  a  greater  space  than  that  between 
other  figures  may  be  used  to  separate  a  number  into  periods. 

Thus,  twenty-five  thousand  four  hundred  twenty-one  may  be  written 
25,421  or  25  421. 


ORAL  EXERCISE 

.Head  aloud  the  following  numbers: 

1.  1,482.  3.  375,214.  5.  8217000214. 

2.  7,009.  4.  278,900.  6.  7000421817. 


4  PRACTICAL   BUSINESS   ARITHMETIC 

10.  For  convenience  in  reading,  the  successive  orders  of  units 
are  divided  into  groups  of  three  figures  each,  called  periods. 
The  first  four  periods  are  shown  in  the  following  numeration 
table.  The  number  used  for  illustration  is  sixty-seven  billion, 
four  hundred  twenty-one  million,  five  thousand,  two  hundred 
sixteen,  and  seven  hundred  fifty-one  thousandths. 

NUMERATION  TABLE 

PERIODS  :  Billions         Millions      Thousands        Units  Thousandths 


°RDERS: 


33        2     a    •=       '3        a     3 


o     H        o        s 


W    H    £>       H    H    P       M    H    £>       K    H    t>       Q       H    M    H 

67,     421,     005,     216      .      751 

11.  In  reading  integers  do  not  use  the  word  and.  In  deci- 
mal fractions  and  has  an  office  to  perform,  and  if  it  is  used  in 
reading  integers,  misunderstandings  may  occur. 

Thus,  400.011  is  read  four  hundred  and  eleven  thousandths ;  but 

.411  is  read /bur  hundred  eleven  thousandths ;  and 
411.        is  read/our  hundred  eleven. 

WRITTEN   EXERCISE 

Write  in  figures  the  following : 

1.  Six  million,  six  thousand,  five. 

2.  Seven  hundred  fifty-three  billion. 

3.  Four  million,  one  hundred  twenty-five. 

4.  Three  hundred  twenty-one  million,  six. 

5.  Three  million  four  dollars  and  five  cents. 

6.  Ten  billion,  one  thousand,  one  hundred  three. 

7.  Twenty-seven  and  one  hundred  twenty-five  thousandths. 

8.  Sixty-two  thousand  and  four  hundred  twenty-five  thou- 
sandths. 

9.  Three  million  four  hundred  twenty  thousand  one  dollars 
and  fifteen  cents. 


NOTATION   AND   NUMERATION  5 

12.    Integers  should  be  read  in  the  shortest  way  possible. 

Thus,  1946  should  be  read  nineteen  hundred  forty-six,  not  one  thousand 
nine  hundred  forty-six.      The  space   for  writing  the  amount  on  a  check, 


ffirst  National  3$ank 


19  __  Y 


Way  to  the 


" 


note,  or  other  business  paper  is  generally  limited  to  one  line,  and  it  is  im- 
portant that  the  amount  be  expressed  in  the  fewest  words  possible. 

ORAL  EXERCISE 

Head  aloud  the,  following  : 

1.  In  a  recent  year  the  railroad  trackage  of  the  world  was 
about  550,400    mi.,  distributed   as    follows:.   North    America, 
237,600  mi.;    Europe,  179,500  mi.;    Asia,   75,400  mi.;    South 
America   and   West   Indies,  29,100   mi.  ;    Australasia,   16,900 
mi.  ;  Africa,  11,900  mi. 

2.  The    trackage  in  North  America  in   the  same  year  was 
distributed  approximately  as  follows  :   United  States,  208,000 
mi.  ;  British  North  America,  18,900  mi.  ;   Mexico,  9,200  mi.  ; 
Central  America,  900  mi. ;  Newfoundland,  600  mi. 

3.  In  the  same  year  the  railways  of  the  United  States  aggre- 
gated about   one  half   the    total    mileage    of    the    world,    and 
over  this   enormous   trackage   about   44,500   locomotives   and 
1,562,900   coaches  and  cars  carried  about  696,950,900  passen- 
gers and  1,306,628,800  tons  of  freight. 

4.  In  the  same  year  the  aggregate  capital   stock    of   these 
railways  was  about  16,500,000,000,  the  gross  earnings    about 
81,908,800,000,  and  the  net  earnings  8592,509,000. 


6  PRACTICAL    BUSINESS   ARITHMETIC 

THE   ROMAN   SYSTEM 

ORAL   EXERCISE 

1.  Make  a  list  of  the  Roman  numerals  used  in  the  headings 
marking  the  divisions  of  this  book,  and  read  the  list  so  prepared. 

2.  What  symbol  ordinarily  appears  on  a  watch  face  for  four? 

13.  This  system  of  writing  numbers  is  called  Roman  notation 
because    it  was  first  used  by  the  Romans.     It   is    now  rarely 
used  except  for  numbering  books  and  their  parts,  for  writing 
inscriptions  on    buildings,  and  for  marking  the  hours  on  the 
dials  of  clocks  and  watches.     It  employs  seven  capital  letters  : 

I  V  X  L  C  D  M 

1  5  10  50  100  500          1000 

14.  Other  numbers  are  expressed  by  a  combination  of  these 
letters  on  the  general  principle  that 

A  combination  of  letters  arranged  from  left  to  right  in  the  order 
of  value  is  equal  to  the  sum  of  the  constituent  letters. 

15.  But  the   use  of   the  same  letter  four  or  more  times  is 
avoided  by  employing  the  sub-principle  that 

When  one  letter  precedes  another  of  greater  value  the  value  of 
the  two  is  that  of  their  difference. 

Thus,  II  =  2  ;  VIII  =  8 ;  and  CCC  =  300.      But  IV  or  IIII  =  4 ;  XL  = 
40;  XC  =90;  and  CD  =  400. 

ORAL   EXERCISE 

1.  Multiply  twenty-seven  by  itself  in  Roman  numerals. 

2.  Why  is  the  Arabic  system  better  than  the  Roman  system  ? 

3.  Read    the    following    inscription:     MDCCCXLVIII- 
Charlestown  High  School  — MCMVI. 

Nineteen  hundred  was  formerly   written  MDCCCC,  but  it  is  now  often 
written  MCM. 

4.  Read  the  following  numbers  of  chapters  in  a  book  :  XXIX, 
XXXVIII,  LXIX,  LII,  LXVII,  LXXVI,  LXXIX,  CLIII. 

5.  Read    the    following    numbers    of    years  :     MDCCXCV, 
MCMVII,  MDCCLXXVI,  MCMIX,  MDCCCXCVIII. 


NOTATION    AND   NUMERATION  7 

WRITTEN  EXERCISE 

1.  Write  in  the  Roman  system :   19,  88,  99,  124,  1907,  1910, 

2.  Write  the   largest   possible  number  using  the  six  follow- 
ing numerals :   1,  0,  8,  0,  9,  5. 

3.  Write  in  Arabic  numerals    the    following   number :    five 
billion,  two  hundred  seventeen  million,  two  hundred  ten  thou- 
sand, and  fifteen  thousandths. 

4.  Write  in  the  Roman  system  the  following  historical  years  : 
the  discovery  of  America ;  the  landing  of  the  Pilgrim  Fathers 
at  Plymouth ;   the  declaration  of  independence. 

5.  Write   in    Arabic    numerals  the    number   in    problem    3 
increased  by  two  hundred  seventy-one  and  four  hundred  fifteen 
thousandths  ;   diminished  by  two  thousand,  four  hundred  sixty, 
and  eleven  thousandths. 

16.  A  unit  is  a  standard  quantity  by  which  other  quantities 
of  the  same  kind  are  measured. 

The  simplest  form  of  a  unit  is  a  single  entire  thing  by  which  other  simi- 
lar things  can  be  measured  by  integral  enumeration.  Thus,  the  unit  of  dis- 
tance is  an  inch;  a  group  of  12  in.  taken  in  succession  is  a  foot;  3  ft.  is  a 
yard  ;  and  so  on. 

17.  Numbers  that  have  units  of  the  same  kind  are    called 
like  numbers. 

Thus,  $12  and  $15,  and  8  hr.  and   3  lir.,  are  like   numbers. 

ORAL  EXERCISE 
Name  the  unit  in  each  of  the  following  : 

1.  A  barrel  of  sugar  sold  by  the  pound. 

2.  A  car  load  of  apples  bought  by  the  barrel. 

3.  A  car  load  of  lumber  sold  by  the  thousand  feet. 

4.  Sixty-four  thousand  bricks  sold  by  the  thousand. 

5.  Forty  and  one-half  yards  of  carpet  sold  by  the  yard. 

6.  Twenty-five  hundred   pounds   of   beef   bought   by   the 
hundredweight.  t 

7.  When  the  value  in  a  five-dollar  gold  piece  is  thought  of, 
what  is  the  unit  ? 


CHAPTER   III 

* 

UNITED    STATES    MONEY 
ORAL  EXERCISE 

Read  the  following  expressions,  supplying  the  missing  word  or 
words : 

1.  The  denominations  of  United  States  money  used  in  busi- 
ness are  dollars, ,  and . 

2. mills  or cents  equal  one  dollar. 

3.  The is  not  a  coin,  but  it  is  sometimes  used  in  mak- 
ing calculations. 

4.  The  first  two  figures  at  the  right  of  dollars  denote , 

and  the  third  figure  denotes . 

5.  The  two  figures  denoting  cents  express of  a  dollar ; 

the  figure  denoting  mills  expresses of  a  dollar. 

6.  One  thousandth  of  a  dollar  is mill ;  seven  mills  are 

of  a  dollar. 

7.  Fifteen  hundredths  of  a  dollar  are ;  nine  tenths 

of  a  dollar  are  nine or cents. 

8.  $25  = t\    3700^  =  i ;    $17.85  = *;   4925^ 


9.  State  a  short  method  of  reducing  dollars  to  cents ;  dol- 
lars and  cents  to  cents  ;  cents  to  dollars. 

18.  The  following  kinds  of  currency  are  in  daily  use  in  the 
United  States  at  the  present  time  :  gold  coins ;  silver  dollars ; 
subsidiary  coins  (small  change) ;  gold  certificates ;  silver  cer- 
tificates; United  States  notes  and  treasury  notes  of  1890; 
national  bank  notes. 

The  coins  now  authorized  by  the  United  States  government  are  as  follows-? 

1.  The  gold  double  eagle,  eagle,  half  eagle,  and  quarter  eagle. 

2.  The  silver  dollar,  half  dollar,  quarter  dollar,  and  dime. 

3.  The  nickel  five-cent  piece  and  the  bronze  one-cent  piece. 


UNITED    STATES   MONEY  9 

19.  Gold  or  silver  in  bars  or  ingots  is  called  bullion. 
The  paper  money  of  the  United  States  is  at  present  as  follows : 

1.  Gold  certificates,  issued  for  gold  deposited  in  the  U.  S.  Treasury. 

2.  Silver  certificates,  issued  for  silver  deposited  in  the  U.  S.  Treasury. 

3.  United  States  notes  (greenbacks),  promises  of  the  government  to  pay  to 
the  holder  on  demand  a  definite  number  of  gold  or  silver  dollars. 

4.  National  bank  notes,  issued  by  national  banks  under  the  supervision 
of  the  National  Government.     These  notes  are  secured  by  U.  S.  bonds  and 
are  redeemable  on  demand  in  lawful  money. 

5.  Treasury  notes,  which  were  issued  for  silver  bullion  deposited  in  the 
U.  S.  Treasury.      These  notes  are  not  now  issued. 

ORAL  EXERCISE 

1.  What  is  meant  by  money,  currency,  legal  tender? 

In  such  exercises  as  the  above  the  student  should  not  try  to  repeat  defini- 
tions, but  should  explain  the  terms  in  his  own  way. 

2.  Name  the    gold  "coins  of   the  United   States;    the  silver 
coins ;  the  paper  money  ;  give  the  value  of  each  of  the  gold  coins. 

3.  Read  in  three  ways :  14.8665;  I25.87J;  1178.475. 

4.  Name  the  largest  gold  and  silver  coins  that  will  exactly 
express  each  of  the  following  amounts:  127.95;  §28.24;  $75.82. 

20.  When  it  is  desirable  to  express  United  States  money  in 
written  words,  the  cents  should  be  written  in  fractional  form, 
as  in  the  following  note  : 


CHAPTER  IV 

ADDITION 
ORAL  EXERCISE 

1.  Find  the  sum  of  1,  2,  3,  4,  5,  6,  7,  8,  and  9. 

2.  Read  each  of  the  numbers  in  problem  1  increased  by  2  ; 
by  5;  by  3;  by  7  ;   by  8;  by  9 ;   by  17;   by  23. 

^3.    Find  the  sum  of  8,  7,  9,  5,  6,  11,  and  12. 

4.  Read  each  of  the  numbers  in  problem  3  increased  by  12; 
by  15;  by  18;  by  24 ;  by  42;  by  19;  by  16. 

5.  Illustrate  what  is  meant  by  like  numbers. 

21.  Only   like  numbers  can  be  added. 

22.  To  secure  speed  and  accuracy  in  addition  name  results 
only  and  express  these  in  the  fewest  words  possible. 

Thus,  in  adding  2,  4,  7,  8,  3,  2,  and  8  say  6,  13,  21,  4,  6,  34 ;   do  not  say 
2  and  4  are  6  and  7  are  13  and  8  are  21  and  3  are  24  and  2  are  26  and  8  are  34. 

ORAL  EXERCISE 

Name  the  sum  in  each  of  the  following  problems : 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

3 

2 

2 

8 

1 

5 

8 

1 

3 

5 

5 

1 

3 

4 

2 

2 

1 

4 

2 

3 

2 

2 

3 

3 

1 

4 

7 

2 

5 

7 

1 

6 

3 

1 

6 

1 

3 

6 

4 

6 

4 

2 

J 

2 

3 

2 

8 

2 

2 

4 

3 

7 

4 

2 

2 

3 

7 

5 

8 

5 

8 

4 

1 

3 

4 

4 

4 

9 

8 

7 

2 

3 

2 

6 

4 

4 

8 

4 

4 

3 

7 

7 

5 

3 

3 

1 

4 

8 

4 

2 

5 

6 

3 

5 

2 

2 

3 

8 

6 

2 

0 

5 

2 

5 

1 

6 

0 

6 

2 

3 

1 

4 

2 

2 

5 

7 

2 

6 

3 

4 

3 

8 

1 

7 

7 

6 

1 

1 

1 

1 

7 

7 

1 

2 

3 

3 

6 

2 

2 

4 

2 

2 

4 

3 

4 

2 

1 

1 

1 

2 

2 

2 

3 

5 

1 

8 

3 

2 

2 

3 

1 

3 

8 

6 

2 

4 

1 

5 

1 

2 

3 

2 

4 

1 

2 

4 

4 

9 

8 

7 

id 


ADDITION  11 

23.  Addition  is  the  basis  of  all  mathematical  processes.     It 
constitutes  a  large  part  of  all  the   computations  of  business 
life   and   concerns,  to   some   extent,  every  citizen   of   to-day. 
Ability  to  add  rapidly  and  accurately  is  therefore  a  valuable 
accomplishment. 

24.  Rapid  addition  depends  mainly  upon  the  ability  to  group  ; 
that  is,  to  instantly  combine  two  or  more  figures  into  a  single 
number.     In  reading  it  is  never  necessary  to  stop  to  name  the 
individual  letters  in  the  words.     All  the  letters  of  a  word  are 
taken  in  at  a  glance  ;  hence  the  whole  word  is  known  at  sight. 
Words  are  then  grouped  in  rapid  succession  and  a  whole  line 
is  practically  read  at  a  glance.     This  is  just  the  principle  upon 
which   rapid    addition    depends.       From  two  to  four  figures 
should  be  read  at  sight  as  a  single  number,  and  the  group  so 
formed  should  be  rapidly  combined  with  other  groups  until  the 
result  of  any  given  column  is  determined.     This  can  be  done 
only  by  intelligent,  persistent  practice. 

25.  The  following  list  contains  all  possible  groups  of  two 
figures  each. 

ORAL   EXERCISE 

Pronounce  at  sight  the  sum  of  the  following  groups: 
a       b         cd        e        f        g       h        i        j        klmno 

1.  11224133'4314247 
13121523^673567 

2.  898564557156689 
^  £  8  £  i  i  i  i  ^  5  ?  5  ^  £  i 

3.  877497675324576 

235838799899842 


The  above  exercise  may  be  copied  on  the  board  and  each  student  in  turn 
required  to  name  the  results  from  left  to  right,  from  right  to  left,  from  top 
to  bottom,  and  from  bottom  to  top.  The  drill  should  be  continued  until 
the  sums  can  be  named  at  the  rate  of  150  per  minute.  This  is  the  first 
and  most  important  step  in  grouping. 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

Name  the  sum  in  each  of  the  following  problems  : 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

6 

7 

3 

5 

6 

7 

9 

9 

9 

1 

2 

5 

8 

2 

8 

3 

1 

4 

2 

4 

7 

9 

8 

8 

4 

7 

2 

3 

7 

2 

8 

7 

7 

5 

8 

2 

5 

9 

4 

5 

8 

3 

5 

4 

1 

7 

'9 

6 

9 

3 

9 

8 

4 

7 

1 

1 

7 

9 

5 

9 

3 

8 

5 

3 

8 

1 

6 

4 

9 

2 

6 

5 

7 

3 

4 

9 

4 

7 

7 

2 

9 

8 

5 

1 

3 

5 

7 

6 

5 

5 

5 

6 

6 

8 

2 

4 

4 

3 

6 

3 

6 

8 

7 

4 

6 

5 

6 

5 

5 

7 

5 

4 

2 

1 

3 

6 

4 

9 

4 

8 

2 

3 

2 

1 

1 

2 

3 

1 

1 

2 

5 

3 

8 

1 

9 

4 

3 

3 

1 

4 

2 

1 

5 

6 

4 

5 

9 

7 

6 

6 

Name  the  results  only  and  make  groups  of  two  figures  each.  Thus,  in 
problem  1,  beginning  at  the  bottom  and  adding  up,  say  6,  16,  28,  43,  52. 

16-45.  Add  the  numbers  in  the  exercise  on  page  10  by 
groups  of  two  figures  each. 

26.  It  is  practically  as  easy  to  add  54  and  9,  59  and  6,  etc., 
as  it  is  4  and  9,  9  and  6,  etc.  4  and  9  are  always  equal  to  1 
ten  and  3  units, and  9  and  6  to  1  ten  and  5  units.  Hence  in 
adding  54  and  9  think  of  the  tens  as  increased  by  1,  call  the 
units  3,  and  the  result  is  63 ;  in  adding  59  and  6  think  of  the 
tens  as  6,  the  units  as  5,  and  the  result  as  65. 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups  : 
i.  27    48    59    77    58    52    59    75    95    84    39    59    84    76    91 


2.  75   59    77    88    74    23    24    44    89    78    67    37    56    58    68 
J^J^_^J>J>_^J?1J?-1_?-1-1    —    - 

3.  37    49    38    37    45    95    98    87    54.   72    63    42    73    97  88 

587698779989859 


ADDITION  13 

27.  In  combining  numbers  between  10  and  20  think  of  them 
as  one  ten  and  a  certain  number  of  units  and  not  as  a  certain 
number  of  units  and  1  ten. 

Thus,  in  combining  17  and  18  think  of  28  and  7,  or  35;  in  combining  19 
and  15  think  of  29  and  5,  or  34  ;  and  so  on. 

ORAL   EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups  : 
abcde        fghi        jklmno 

1.  12    17    12    16    11    12    18    16    17    11    19    13    18    12    17 
1517121314111812181915    13    121419 

2.  13    11    15    19    14    19    17    15    13    19    16    14    18    18    12 


3.  11    17    12    17    15    15    12    18    16    14    19    14    19    17    11 
111413131715171616131918131115 

The  above  exercise  contains  all  combinations  possible  with  the  numbers 
from  11  to  19  inclusive.  Drill  on  the  exercise  should  be  continued  until  re- 
sults can  be  named  at  the  rate  of  120  per  minute. 

23.  Numbers  between  10  and  20  may  be  combined  with  num- 
bers above  20  in  practically  the  same  manner  as  in  §  27 

Thus,  in  adding  62  and  12  think  of  72  and  2,  or  74;  in  adding  79  and  17 
think  of  89  and  7,  or  96. 

ORAL   EXERCISE 

Pronounce  at  sight  the  sum  of  the  following  numbers.: 

1.  25    48    59    87    91    75    86    75    48    78    57    89    37    56    75 
nni6U181819121^131614171814 

2.  29  47  83  92  36  54  59  78  67  92  77  86  53  78  85 
1314191419^1318151313^191917  1414 

3.  31  32  45  69  74  95  98  92  96  87  86  34  43  64  38 
19  17  19  15   8  18  14  19  15  17  19  18  18  19  17 


14  PRACTICAL   BUSINESS    ARITHMETIC 

ORAL  EXERCISE 

1.  Count  by  7's  from  1  to  85. 

SOLUTION.     8,  15,  22,  9,  36,  43,  50,  7,  64,  71,  8,  85. 

Count  by : 

2.  2's  from  39  to  55.  14.  8's  from  10  to  138. 

3.  5's  from  11  to  86.  15.  7's  from  19  to  152. 

4.  6's  from  15  to  63.  16.  6's  from  20  to  128. 

5.  5's  from  2  to  107.  17.  6's  from  15  to  111. 

6.  7's  from  11  to  60.  18.  9's  from  12  to  102. 

7.  8's  from  25  to  89.  19.  8's  from  17  to  113. 

8.  9's  from  31  to  112.  20.  7's  from  24  to  108. 

9.  8's  from  32  to  192.  21.  6's  from  27  to  117. 

10.  7's  from  18  to  102.  22.    4's  from  19  to  183. 

11.  6's  from  72  to  126.  23.    ll's  from  14  to  102. 

12.  9's  from  10  to  136.  24.    12's  from  17  to  161. 

13.  9's  from  17  to  152.  25.    13's  from  17  to  121. 
26.  Beginning  at  1  count  by  4's  to  17  ;  going  on  from  17 

count  by  7's  to  52  ;  from  52  count  by  9's  to  133  ;  from  133 
count  by  5's  to  158  ;  from  158  count  by  12's  to  206  ;  from 
206  count  by  13's  to  271. 

This  exercise  furnishes  one  of  the  best  possible  drills  in  addition,  and  it 
should  be  continued  until  the  successive  results  can  be  named  at  the  rate  of 
150  per  minute. 

29.  If  the  student  is  accurate  and  rapid  in  making  groups 
of  two  figures  each,  he  is  ready  for  practice  in  groups  of  three 
figures  each.  In  the  following  exercise  are  all  the  possible 
groups  of  three  figures  each. 

ORAL  EXERCISE 

Name  at  sight  the  sum  of  each  of  the  following  groups: 

4,  2,  and  3  should  be  thought  of  as  9  just  as  p-e-n  is  thought  of  as  pen. 

l.  419811318145178 
131223173314414 
332175631941641 


ADDITION  15 


2. 

1 

6 

1 

4 

1 

2 

1 

1 

1 

1 

7 

6 

9 

8 

1 

4 

1 

2 

1 

2 

2 

9 

1 

1 

6 

6 

6 

5 

5 

5 

9 

2 

5 

2 

3 

1 

1 

8 

7 

8 

1 

1 

1 

1 

7 

3. 

6 

5 

2 

5 

2 

3 

9 

2 

2 

2 

2 

6 

1 

1 

2 

1 

1 

3 

3 

3 

2 

2 

8 

7 

6 

5 

1 

1 

1 

2 

5 

5 

6 

2 

4 

3 

2 

2 

2 

2 

2 

1 

5 

4 

4 

4. 

3 

2 

1 

2 

2 

6 

2 

6 

5 

5 

7 

1 

1' 

1 

1 

2 

2 

1 

7 

6 

8 

6 

2 

2 

2 

2 

1 

1 

6 

9 

2 

2 

3 

7 

9 

2 

7 

6 

9 

8 

5 

2 

1 

9 

9 

5. 

9 

8 

9 

8 

7 

3 

4 

5 

6 

6 

5 

4 

3 

3 

4 

1 

1 

1 

1 

1 

5 

8 

7 

7 

7 

5 

4 

4 

4 

4 

8 

8 

7 

7 

7 

5 

4 

5 

9 

8 

6 

7 

9 

8 

6 

6. 

5 

6 

6 

9 

5 

7 

3 

4 

9 

6 

6 

8 

3 

3 

3 

5 

7 

6 

4 

4 

3 

4 

4 

4 

8 

7 

4 

9 

4 

4 

5 

7 

9 

9 

4 

4 

6 

4 

8 

6 

6 

8 

9 

5 

4 

7. 

3 

4 

6 

9 

8 

5 

4 

3 

3 

2 

3 

3 

4 

5 

8 

8 

7 

6 

9 

9 

9 

7 

8 

3 

5 

3 

7 

7 

8 

8 

9 

9 

6 

9 

9 

9 

8 

8 

9 

6 

8 

9 

7 

9 

8 

8. 

8 

5 

4 

3 

3 

5 

2 

3 

3 

4 

5 

7 

7 

5 

4 

8 

8 

9 

8 

7 

2 

4 

3 

7 

6 

7 

9 

8 

7 

6 

9 

5 

6 

7 

3 

5 

9 

6 

7 

8 

9 

9 

9 

8 

7 

9. 

3 

3 

2 

2 

3 

3 

4 

5 

7 

9 

9 

9 

7 

3 

6 

6 

3 

4 

4 

3 

6 

6 

7 

8 

7 

6 

5 

6 

3 

4 

9 

5 

8 

7 

4 

8 

6 

7 

8 

7 

5 

4 

3 

3 

2 

10. 

2 

2 

3 

4 

5 

7 

2 

2 

3 

4 

5 

7 

9 

6 

6 

4 

9 

6 

5 

6 

7 

4 

8 

5 

5 

6 

7 

9 

6 

5 

5 

9 

6 

8 

8 

8 

4 

9 

9 

7 

7 

7 

6 

5 

4 

11. 

8 

8 

9 

2 

2 

3 

4 

5 

6 

8 

8 

9 

6 

8 

7 

6 

8 

3 

3 

7 

5 

5 

5 

8 

8 

5 

4 

5 

7 

3 

3 

2 

2 

8 

9 

7 

5 

9 

9 

6 

6 

4 

3 

2 

2 

This  exercise  should  be  drilled  upon  until  the  sums  of  the  groups,  in  any 
order,  can  be  named  at  the  rate  of  120  per  minute. 


16  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1-15.    Turn  to  the  exercise  on  page  10  and  find  the  sum  of 
the  numbers  given. 

Name  results  only,  and  make  groups  of   three  figures  each.     Thus,  in 
problem  1,  say  9,  23,  37,  43. 

Add  from  the  bottom  up  and  check  the  work  by  adding  from  the  top  down. 
Find  the  sum  of  the  following  problems  : 
16.     17.     18.     19.     20.     21.     22.     23.     24.     25.     26.     27.     28.     29.     30. 

131422244512954 


1 

1 

3 

3 

3 

1 

6 

3 

9 

5 

7 

4 

0 

7 

3 

1 

1 

4 

1 

5 

2 

2 

4 

5 

0 

2 

4 

1 

2 

1 

2 

1 

3 

1 

3 

1 

4 

1 

8 

8 

9 

2 

8 

0 

1 

2 

4 

1 

4 

6 

4 

5 

8 

3 

2 

0 

3 

0 

0 

6 

2 

2 

3 

8 

1 

1 

2 

1 

7 

1 

1 

5 

2 

5 

8 

2 

4 

2 

2 

2 

2 

2 

3 

8 

3 

5 

7 

2 

6 

1 

5 

2 

1 

4 

5 

3 

7 

6 

2 

7 

3 

7 

2 

6 

6 

1 

2 

9 

4 

3 

2 

3 

1 

8 

2 

2 

1 

6 

0 

7 

5 

1 

8 

3 

4 

2 

1 

2 

9 

9 

6 

7 

2 

3 

3 

3 

5 

2 

3 

3 

6 

9 

3 

3 

1 

2 

8 

2 

6 

3 

1 

3 

1 

3 

3 

1 

0 

5 

6 

3 

7 

0 

4 

1 

1 

3 

2 

7 

2 

4 

3 

0 

2 

8 

8 

4 

7 

2 

5 

9 

5 

4 

2 

5 

2 

4 

8 

5 

1 

2 

3 

3 

2 

3 

2 

2 

4 

1 

4 

4 

3 

2 

2 

0 

4 

3 

0 

5 

2 

1 

1 

2 

1 

2 

6 

6 

4 

4 

6 

6 

3 

6 

2 

5 

8 

8 

6 

2 

3 

3 

8 

5 

2 

4 

4 

3 

3 

2 

8 

2 

1 

2 

6 

5 

1 

1 

1 

3 

0 

5 

6 

1 

6 

2 

1 

4 

4 

1 

3 

7 

2 

9 

3 

7 

9 

1 

5 

7 

5 

7 

3 

5 

2 

2 

2 

6 

2 

2 

3 

1 

7 

3 

3 

7 

2 

4 

2 

5 

6 

1 

3 

1 

3 

0 

3 

2 

2 

1 

3 

1 

4 

2 

1 

2 

1 

2 

2 

7 

7 

7 

1 

1 

9 

2 

2 

9 

7 

2 

2 

3 

8 

3 

1 

& 

3 

9 

1 

2 

5 

2 

1 

3 

4 

4 

4 

1 

7 

7 

1 

0 

0 

8 

4 

8 

4 

2 

1 

3 

7 

3 

2 

5 

7 

6 

5 

5 

2 

4 

4 

3 

1 

6 

2 

1 

5 

5 

3 

2 

3 

2 

8 

1 

3 

6 

3 

2 

3 

1 

1 

2 

1 

1 

2 

1 

2 

1 

5 

7 

1 

1 

ADDITION 


17 


30.  It  is  always  an  advantage  to  find  groups  of  figures  aggre- 
gating 10  and  20  in  the  body  of  a  column. 

These  groups  should  be  added  immediately  to  the  sum  already  obtained 
by  simply  combining  the  tens  of  the  two  numbers.  It  is  not  a  good  plan, 
however,  to  take  the  digits  in  irregular  order  in  order  to  form  groups  of 
10  and  20. 

ORAL  EXERCISE 

Find  the  sum  of  the  following  problems,  taking  advantage  of 
groups  of  10  and  %0  wherever  possible  : 
1.       2.       3.       4.       5.      6.      7.      8.      9.     10.      11.     12.     13.    14.    15. 


11  21 

9J  8j 

I) 

6525343   7   8   259 
455432554   789 

71  41 
3J  6J 

!) 

185678556   321 
9279874   0   2   581 

2   7 

7 

2431236   9   7525 

16.  17. 

18. 

19.  20.  21.  22.  23.  24.  25.  26.  27.  28.  29.  30. 

4]  11 

91 

146571244161 

8   1 

>  2 

612224223931 

3J  8J 

9J 

352315643218 

7]  i 

4 

654475187870 

2   6 

>  1 

224335762349 

lJ  3, 

5, 

232344245750 

6   5 

9 

244866531811 

31.  32. 

33. 

34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.  45. 

2   3^ 

91 

866665866276 

2]  8 

4 

567757439897 

9   9. 

7. 

687868985994 

9J  7 

9 

979787796929 

46.     47.     48.     49.     50.      51.     52.    53.    54.    55.    56.    57.    58.  59.    60. 

38     42     25     35     46     14     21     12    18    29    57  17    13    14    15 


32554627 
34768672 
84898858 
67455236 


18 


PRACTICAL   BUSINESS   ARITHMETIC 


31.  When  three  figures  are  in  consecutive  order  the  sum  may 
be  found  by  multiplying  the  middle  figure  by  3 ;  when  five 
figures  are  in  consecutive  order  the  sum  may  be  found  by  mul- 
tiplying the  middle  figure  by  5 ;  etc. ;  or  the  sum  of  any  num- 
ber of  consecutive  numbers  may  be  found  by  taking  one  half  the 
sum  of  the  first  and  last  numbers  and  multiplying  it  by  the 
number  of  terms. 

ORAL   EXERCISE 

By  inspection  find  the  sum  of: 
1.     2.       3.       4.       5.       6.       7.       8.       9.      10.     11.      12.     13.     14.     15. 

7  10    13    16    19    22    25    28    31    34     37     40     43     46     49 

8  11    14    17    20    23    26    29    32    35     38     41     44     47     50 

9  12    15    18    21    24    27    30    33    36     39     42     45     48     51 


16. 

17. 

18. 

19. 

20. 

21. 

22. 

23. 

24. 

25. 

26. 

27. 

28. 

29. 

30. 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

80 

11 

16 

21 

26 

31 

36 

41 

46 

51 

56 

61 

66 

71 

76 

81 

12 

17 

22 

27 

32 

37 

42 

47 

52 

57 

62 

67 

72 

77 

82 

13 

18 

23 

28 

33 

38 

43 

48 

53 

58 

63 

68 

73 

78 

83 

14 

19 

24 

29 

34 

39 

44 

49 

54 

59 

64 

69 

74 

79 

84 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

38. 

39. 

40. 

41. 

42. 

43. 

44. 

45. 

7 

10 

13 

16 

19 

22 

25 

28 

31 

34 

37 

40 

43 

46 

49 

8 

11 

14 

17 

20 

23 

26 

29 

32 

35 

38 

41 

44 

47 

50 

9 

12 

15 

18 

21 

24 

27 

30 

33 

36 

39 

42 

45 

48 

51 

10 

13 

16 

19 

22 

25 

28 

31 

34 

37 

40 

43 

46 

49 

52 

11 

14 

17 

20 

23 

26 

29 

32 

35 

38 

41 

44 

47 

50 

53 

12 

15 

18 

21 

24 

27 

30 

33 

36 

39 

42 

45 

48 

51 

54 

13 

16 

19 

22 

25 

28 

31 

34 

37 

40 

43 

46 

49 

52 

55 

14 

17 

20 

23 

26 

29 

32 

35 

38 

41 

44 

47 

50 

53 

56 

15 

18 

21 

24 

27 

30 

33 

36 

39 

42 

45 

48 

51 

54 

57 

16 

19 

22 

25 

28 

31 

34 

37 

40 

43 

46 

49 

52 

55 

58 

17 

20 

23 

26 

29 

32 

35 

38 

41 

44 

47 

50 

53 

56 

59 

32.    When  a  figure  is  repeated  several  times  the  sum  may  be 
found  by  multiplication. 


ADDITION  19 

ORAL  EXERCISE 

By  inspection  find  the  sum  of  the  following  groups : 
1.      2.       3.      4.       5.       6.       7.      8.        9.      10.      11.     12.     13.     14.     15. 


4   3 

4 

5 

3 

7 

8 

8 

15 

6 

7 

8  15  13 

9 

9   7 

4 

5 

3 

7 

5 

7 

15 

6 

8 

7  14  13 

8 

9   8 

4 

5 

9 

7 

5 

9 

15 

12 

7 

8  15  13 

8 

9   8 

9 

5 

9 

8 

6 

9 

8 

12 

7 

7  14   7 

9 

9   8 

9 

9 

8 

8 

6 

9 

8 

12 

7 

8  15   7 

8 

16.   17.   18.     19.     20.     21.    22.     23.      24.      25.     26.     27.     28.     29.     30. 

374275     12       2468985     16 


3      7 

4 

2      7 

5 

5 

2 

4 

6 

8 

9 

8 

5     16 

3      7 

4 

2      4 

5 

5 

2 

4 

6 

8 

9 

8 

5     16 

2      2 

7 

8      4 

4 

5 

3 

5 

4 

3 

5 

8 

5     16 

2      2 

7 

8      2 

4 

5 

3 

5 

4 

3 

5 

8 

5     20 

2      2 

7 

8      2 

4 

5 

3 

5 

4 

3 

5 

9 

8       1 

33.  In  all  written  work  make  plain,  legible  figures  of  a 
uniform  size,  write  them  equal  distances  from  each  other, 
and  be  sure  that  the  units  of  the  same  order  stand  in  the 
same  vertical  column. 


7 


34.  Many  of  the  errors  that  occur  in  business  are  in  simple 
addition.      Errors  in   addition   result   from   two   main  causes  : 
irregularity  in  the  placing  of  figures  ;   poor  figures. 

35.  In  business  it  is  important  that  figures  be  made  rapidly  ; 
but  rapidity  should  never  be  secured  at  the  expense  of  legibility. 

WRITTEN   EXERCISE 

Copy  and  find  the  sum  of: 

1.  2.  3.  4.  5.  6. 

1745  1842  1249  4271  6229  1481 

1862  1695  1810  8614  4813  1862 

7529  4716  6241  9217  7142  4129 

8721  8412  1728  8214  6212  2412 


20 


PRACTICAL   BUSINESS    AKITHMETIG 


7. 

8. 

9. 

10. 

11. 

12. 

4216 

2110 

4142 

1061 

4113 

4112 

8912 

8420 

4347 

1875 

8217 

1012 

4729 

1641 

1012 

6214 

8614 

1862 

8624 

1722 

1816 

1931 

1692 

1721 

4829 

1837 

4112 

1648 

1591 

1692 

6212 

4216 

4210 

1721 

1686 

1486 

4110 

4117 

1618 

1728 

2172 

4112 

4210 

1832 

4060 

1421 

1754 

1010 

36.  The  simplest  way  to  check  addition  is  to  add  the  columns 
in  reverse  order.     If   the  results  obtained  by  both   processes 
agree,,  the  work  may  be  assumed  to  be  correct. 

37.  In  adding  long  columns  of  figures  it  is  generally  advis- 
able to  record  the  entire  sum  of  each  column  separately  ;  then 
if  interruptions  occur,  it  will  not  be  necessary  to  re-add  any  por- 
tions already  completed.     After  the  total  of  each  column  has 
been  found  the  entire  total  may  be  determined  by  combining 
the  separate  totals  of  the  columns. 

38.  The  best  way  to  test  the  accuracy  of  columns  added  in  this 
manner  is  to  begin  at  the  left  and  repeat  the  addition  in  reverse 
order.     The  entire  total  of  each  column  should  again  be  written 
and  the  complete  total  of  the  problem  found  by  adding  the  sepa- 
rate totals  of  the  several  columns.     If  the  results  obtained  by 
the  tw^Q  processes  agree,  the  work  may  be  assumed  to  be  correct. 

39.  Example.    Find  the  sum  of  54669,  15218,  36425,  45325, 
and  68619.     Check  the  result. 

SOLUTION.  Beginning  at  the  bottom  of  the 
right-hand  column,  add  each  column  in  regu- 
lar order  and  write  the  entire  totals  as  shown 
in  (a).  Beginning  at  the  top  of  the  left- 
hand  column  again  add  each  column  and 
write  the  entire  totals  as  shown  in  (6).  Next 
add  the  totals  obtained  by  the  first  and 
second  additions  and  compare  the  results. 
Since  the  total  shown  by  (a)  is  equal  to  the 
total  shown  by  (&),  the  result,  220,256,  is  assumed  to  be  correct, 
addition  should  be  carefully  checked. 


(*) 

19 
28 
21 
12 
36 

54669 
15218 
36425 
45325 

68619 

(a) 
36 
12 
21 
28 
19 

220256 

220256 

med  to  be 

220256 

correct.     All  work  in 

ADDITION  21 

WRITTEN  EXERCISE 

See  how  many  times  the  following  numbers  can  be  written  in 
one  minute.      Write  each  number  in  form  for  vertical  addition. 

1.  426579.  3.  17983.21.  5.  170812.34. 

2.  123987.  4.  14080.91.  6.  $41182.50. 

Thus,  in  repeating  the  number  in  problem  1  write  it  as  follows: 

*t  2.  6  J~  7  # 

^  z  6  J~  7  7 

*  2-  6  J~  7  <? 

^  Z  £  J~  7  7 


Be  sure  that  the  spacing  between  the  lines  and  between  the  columns  is 
uniform.  Increase  the  speed  gradually  until  from  150  to  200  figures  can 
be  written  per  minute. 

40.  Skill  in  writing  figures  from  dictation  should  be  culti- 
vated.    The  dictation  should  be  slow  at  first,  but  it  should  be 
gradually  increased  until  the  requisite  speed  is  acquired. 

41.  In  calling  off  numbers  to  another  great  care  should  be 
taken    in    order  that    no    errors  may  be    made.     In  reading 
United  States  money  the  word  dollars  should  be  called  with 
each  amount.     The  word  cents  may  be  omitted  in  all  cases 
except  where  there  are  no  dollars. 

Thus,  in  calling  $400.37  say  four  hundred  dollars,  thirty-seven;  in  calling 
$25.11  say  twenty-five  dollars,  eleven;  in  calling  $1573.86  say  fifteen  hundred 
seventy-three  dollars,  eighty-six;  in  calling  $5.31  say^ye  dollars,  thirty-one. 


WRITTEN  EXERCISE 
Write  from  dictation  and  find  the  sum  of: 

1.  $75.18,  $123.95,  $147.25,  $9.50,  $181.45,  $172.16,  184.98, 
$314.95,  $49.10,  $69.90,  $312.60,  $415.90. 

2.  $3140.19,  $310.92,  $3164.96,  $3162.19,  $18.62,  $410.95, 
$690.18,  $10.75,  $3100.40,  $300.40,  $200.50,  $100.90,  $410.80, 
$100.85,  $310.60,  $80.90,  $399.80,  $412.60. 


22 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN   EXERCISE 

Copy,  find  the  sum,  and  check : 
1.  2. 


/  J  / 


3. 

62  /. 


/  2  &  2 
2  /  J 

2 


/  J  ^j-£  7/*.j-0  /  2J<^2-/ 

37^0  z  6  ^.  /  7 

/  23^.23 

2  £  /  2.4£J  /2J~^2/ 

2  /  2.J-~t£  /  3  2  / 

^  & ^. /  (,  2/^/^2 

2  /  &.J~4^  3  /  J~/  2 

2/  £^.  4Cf  2  /  /  ^"^ 

2^6^62-7. /£  3/7^2^-7.6^    /262^7<^. 


.  67 


/  2 

7< 

2  / 


2 


4. 


6. 


72/2 
/  2 
0  0 


0 


/  2 


2 

2  / 
/  7  2 


£7  2  /.  f  0 


ADDITION  23 

8.  9. 

^ 6 2  /.ttt  //  62-0  /  77.2^~ 
6  f  /  2.0  0  3J~7<f><?.^4:  /  z£,/^z6.^/ 
27 /^./f  /  6^ 2^.7^  /  0/^70  27.60 

/> 

/     r   f  /  / 

~30         37^26/^2         72// 
22  ^ f  ^2.7<T     /  0  Z 
2  6  <?\J~^.rf '0         6>  2  / 

22£^^/.37       7^z^67.^<r      ^/ 

Z  ^ /  6.24?  /  2  0  / 

/  Z  0  7.  /V  6  &  /  2.7 J~ 

372 

/  2  0 
7  ^  6  0.0  0  72  <^j~.  6  ^  /  6  2 

360  ^7.  4^6 

&  <p  *£/  /  £^2      /  /  2  /  4^ ^  0.7 J~ 
72-/20J7//  ^^^76.62 

f2f#J./2-          £2-/#t 

7^/627.03         /  2 
62/26^7^f~        2-/ 7  2 


2  6  /  2  #.  4^J~     /  0  /  2  0  /  b. 

f6<T3~2./7       ^^20/7. 

/  2/20  2.  60  72/26.73 

7- 


22-<s/^.<^2  &  f  J  ^  f.  ^3~  /  &  /  Z 

22tT^.20  70/20.^2  7  2  / 

6  ^3~^.f7  z  77  z 

/  z  6  7  0  z.  6.j~4?  /  f  ^  2 
/26/2J~.6J~      32/6/^.70          6fZ^6.7<f 
/  6  Z  3  & 7'7 &s          2*/ /  2 


24  PRACTICAL   BUSINESS   ARITHMETIC 

42.  Some  accountants  practice  adding  two  columns  at  once 
when  the  columns  are  short.     The  method  generally  employed 
is  similar  to  the  method  explained  for  combining    groups    in 
regular  addition. 

43.  Example.    Find  the  sum  of  83,  72,  89. 

SOLUTION.     Beginning  at  the  bottom  and  adding  up,  think  of  89  and  ^ 

72  as  159  and  2,  or  161  ;  of  161  and  83  as  241  and  3,  or  244. 
In  adding  name  results  only.     Thus  say  159,  161,  241,  244. 

244 

ORAL  EXERCISE 

By  inspection  give  the  sum  of  each  of  the  following  groups : 
1.       2.       3.        4.        5.       6.       7.       8.       9.     10.    11.    12.     13.    14.    15. 

43     64     52     37     65     38    52    85    93    68    58    76    83    57     62 

25  18     29     56     27     43    67    34    72    75    46    39    47    25    39 

16.     17.     18.      19.     20.     21.     22.    23.    24.    25.    26.    27.    28.    29.    30. 

53  52  61  34  91  68  48  24  78  54  94  57  92  76  43 
4643  37  761347699676353644373156 

31.     32.    33.    34.    35.     36.    37.    38.    39.     40.     41.     42.     43.     44.     45. 

65  44  46  48  67  44  53  25  54  46  33  16  67  83  88 
86  57  65  25  48  57  45  31  65  39  64  34  43  82  25 
752134313921676987877725419831 

HORIZONTAL   ADDITION 

44.  In  some  kinds  of  invoicing  arid  in  short-extending  the 
items  of  an  account  numbers  to  be  added  are  written  in  horizon- 
tal lines.     Much  time  may  be  saved  by  adding  these  numbers 
as  they  stand.     After  careful  practice  it  will  be  found  possible 
to   add   numbers   written    in    horizontal   lines  with   as    much 
facility  as  numbers  written  in  vertical  columns. 

45.  In  adding  numbers  written  horizontally  care  should  be 
exercised  to  combine  only  units  of  the  same  order.     It  is  gener- 
ally best  to  add  from  left  to  right  and  to  verify  the  work  from 
right   to   left.     Grouping   may  be    employed  to  advantage  in 
horizontal  addition. 


ADDITION  25 

WRITTEN  EXERCISE 

Copy  and  add  the  following  numbers  horizontally.      Verify  the 

work. 

Thus,  in  problem  1,  beginning  at  the  left,  say  10,  20,  32,  52.  In  verifying 
the  work  from  the  right  say  20,  32,  42,  52. 

1.  8,  2,  1,  1,  7,  1,  4,  6,  2,  3,  8,  9. 

2.  7,  9,  6,  5,  4,  8,  7,  4,  3,  7,  3,  1,  3. 

3.  6,  2,  4,  8,  3,  1,  7,  6,  4,  2,  8,  9,  4,  2. 

4.  15,  23,  46,  83,  29,  35,  42,  15,  21,  26. 

5.  64,  48,  56,  35,  47,  87,  32,  45,  67,  91. 

6.  52,  64,  86,  28,  76,  41,  15,  32,  12,  87. 

7.  32,  48,  24,  62,  85, 14,  63,  54,  78,  94,  23,  45. 

8.  42,  76,  49,  81,  17,  42,  17,  19,  21,  43,  64, 17. 

9.  45,  48,  34,  46,  48,  53,  25,  42,  35,  56,  70,  10. 

10.  291,  196,  855,  578,  210,  354,  102,  232,  241,  162. 

11.  469,  388,  962,  764,  351,  899,  111,  232,  190,  175. 

12.  1525,  5025,  1684,  3142,  8638,  19w  2312,  10*3,  64^  40™. 

It  is  frequently  desirable  to  express  dollars  and  cents  without  the  dollar 
sign  and  the  decimal  point.  This  may  be  done- by  slightly  raising  the  cents 
of  the  amount.  Thus,  $  17.17  may  be  written  1717 ;  $  2.08  may  be  written  208. 

13.  1525,  893,  488,  2184,  1635, 1846,  2914,  4460,  6290,  8460,  4050. 

14.  76<5,  849s  67°5,  95'4,  6863,  5221,  1325,  4218,  6095,  8013,  9062. 

46.  It  is  important  that  the  student  acquire  the  ability  to 
carry  a  series  of  numbers  in  mind.  The  following  exercises 
are  suggestive  of  what  may  be  done  to  cultivate  ability  in  this 
direction. 

The  dictation  suggested  should  not  be  slower  than  at  the  rate  of  one  hun- 
dred twenty  words  per  minute.  Nothing  should  be  written  by  the  students 
until  all  of  the  numbers  of  a  problem  have  been  called  by  the  teacher;  then 
one  student  may  be  sent  to  the  blackboard  and  required  to  write  the  numbers 
from  memory.  If  the  numbers  are  correctly  written,  the  teacher  may  require 
another  student  to  give  the  sum  of  them  without  using  pen  or  pencil.  The 
numbers  may  be  written  on  the  board  in  either  vertical  or  horizontal  order 
as  the  teacher  may  direct. 


26 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL   EXERCISE 

From  the  teacher's  dictation  mentally  find  the  sum  of  each  of  the 
following  problems : 

1.  6,  9,  8,  4,  and  8  are  how  many  ? 

2.  14,  17,  20,  and  5  are  how  many  ? 

3.  24,  17,  16,  and  9  are  how  many? 

4.  5,  6,  7,  1,  and  3  are  how  many  ? 

5.  6,  2,  8,  1,  and  7  are  how  many  ? 

6.  364,  436,  and  657  are  how  many  ? 

7.  438,  212,  and  750  are  how  many  ? 

8.  859,  441,  and  769  are  how  many? 

9.  2140,  3160,  and  4000  are  how  many? 

10.  200,  415,  600,  and  920  are  how  many? 

11.  857,  643,  237,  and  500  are  how  many? 

12.  14150,  14050,  and  $5000  are  how  many? 

13.  $5.15,  $2.15,  and  16.70  are  how  many  ? 

14.  $  167.14,  $232.86,  and  $150  are  how  many  ? 

WRITTEN  REVIEW  EXERCISE 

1.  Find  the  sum  of  all  the  integers  from  2165  to  2260  inclu- 
sive. 

2.  Find  the  sum  of  all  the  integers  from  1137  to  1200  inclu- 
sive. 

3.  Complete  the  following  sales  sheet.     Add    by  columns 
and  by  lines  and  check  the  work  by  adding  the  vertical  and 
horizontal  totals. 

SUMMARY  OF   SALES   FOR   WEEK   ENDING    AUG.    25 


PINK 

OAK 

MAPLE 

SPRITE 

WALNUT 

CHERRY 

TOT  A  L 

Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
Saturday 

121G 
5160 
6152 
1216 
4160 
3165 

18 
40 
18 
18 
80 
80 

16161 
3214 
2150 
2160 
1215 
2115 

47 

90 
18 
50 
40 

72 

649 
316 
163 
130 
315 
218 

58 
40 
59 
98 
16 
50 

860 
160 
430 
115 
218 
165 

40 
50 
17 
67 
90 
37 

315 
513 
968 
413 
411 
118 

64 
80 
52 
60 
50 
50 

186 
216 
756 
314 
132 
17 

50 
54 
14 
75 
75 
05 

_ 

_ 

Total 

ADDITION 


27 


4.    Add   the  following  by  columns  and  by  lines,  and  check 
the  work  by  adding  the  vertical  and  horizontal  totals  : 


21162 

49 

962 

18 

1245 

76 

54168 

97 

52 

19 

176 

19 

1278 

95 

52698 

13 

7529 

87 

95162 

87 

2164 

89 

7524 

16 

47612 

87 

6842 

23 

5948 

23 

76 

95 

87 

14 

2150 

49 

17293 

1745 

86 

51276 

92 

18187 

95 

75 

19 

162 

14 

5290 

18 

9834 

18 

92923 

15 

25 

91 

162 

18 

14 

95 

754 

95 

2167 

92 

2584 

16 

9176 

92 

3164 

82 

1356 

05 

1314 

93 

7125 

95 

2167 

18 

2645 

97 

756 

92 

142 

18 

167 

42 

926 

44 

3167 

18 

75162 

19 

82195 

78 

72162 

18 

9165 

97 

168 

44 

7162 

95 

4167 

18 

7156 

95 

172 

18 

1 

56 

2 

15 

6843 

82 

3954 

05 

60 

65 

9 

18 

8 

85 

9162 

19 

5144 

65 

8162 

18 

91684 

57 

2416 

45 

1829 

32 

4217 

64 

1492 

95 

8647 

64 

168 

94 

257 

16 

417 

86 

952 

17 

347 

18 

5.  Complete  the  following  sales  sheet.  Add  by  columns 
and  by  lines  and  then  check  the  work  by  adding  the  vertical 
and  horizontal  totals. 


SUMMARY   OF   CLERKS'    DAILY   SALES 


^SAMES  OF  CLERKS 

MONDAY 

TUESDAY 

WEDNESDAY 

THURSDAY 

FRIDAY 

SATURDAY 

TOTAL 
FOR  WEEK 

J.  E.  Snow 

167 

18 

194 

67 

98 

46 

241 

80 

175 

66 

314 

90 

W.  B.  Moore 

78 

20 

65 

14 

50 

42 

60 

93 

51 

19 

64 

86 

T.  B.  Welch 

112 

40 

118 

64 

192 

40 

146 

18 

110 

50 

140 

12 

E.  H.  Ross 

164 

90 

143 

18 

192 

64 

214 

10 

110 

60 

190 

18 

Minnie  Davis 

165 

19 

214 

78 

120 

42 

167 

18 

164 

27 

140 

51 

Ada  Bentou 

68 

49 

90 

81 

64 

75 

120 

14 

142 

16 

60 

90 

Elmer  S.  Frey 

240 

18 

920 

41 

718 

52 

167 

59 

840 

72 

143 

86 

Joseph  White 

22 

49 

72 

86 

51 

47 

62 

14 

91 

26 

72 

15 

Margaret  Dix 

47 

26 

91 

18 

21 

64 

18 

42 

61 

19 

64 

86 

F.  O.  Beck 

127 

16 

95 

27 

114 

82 

162 

15 

102 

15 

112 

61 

L.  O.  Avery 

214 

91 

218 

46 

920 

41 

172 

14 

152 

86 

142 

71 

B.  W.  Snyder 

162 

14 

153 

46 

118 

64 

162 

14 

182 

15 

69 

58 

Ella  Harding 

21 

27 

18 

92 

17 

65 

28 

64 

59 

18 

72 

41 

Carrie  Simpson 

21 

18 

45 

30 

16 

98 

42 

41 

20 

68 

75 

98 

W.  F.  Baldwin 

162 

10 

114 

80 

115 

90 

116 

84 

117 

41 

200 

60 

E.  0.  Burrill 

84 

90 

90 

10 

116 

80 

114 

30 

65 

20 

300 

75 

Total 

6.   Without  copying,  find  the  total  population  of  the  United 
States  at  each  census  from  1860  to  1900  inclusive.     Check. 


28 


PRACTICAL   BUSINESS   ARITHMETIC 


POPULATION    OF  THE  UNITED   STATES   AT    EACH   CENSUS  FROM    1800    TO    1900 


STATES  AND  TERRITORIES 

I860 

1S70 

1880 

1890 

1900 

964,201 

996,992 

1,262,595 

1  513  017 

1  828  697 

Alaska                       .     .     . 

33,426 

30,329 

03  592 

Arizona                 .... 

9,658 

40,440 

59,020 

122  931 

Arkansas               .... 

435,450 

484,471 

802,525 

1,128,179 

1,311,504 

California    
Colorado      
Connecticut     
Dakota        ...          .     . 

379,994 
34,277 
400,147 
4,837 

560,247 
39,804 
537,454 
14,181 

864,694 
194,327 
622,700 
135,177 

1,208,130 
419,198 
740,258 

1,485,053 
539,700 
908,420 

Delaware 

112,216 

125,015 

146,608 

168  493 

184,735 

District  of  Columbia      .     . 
Florida  .                         .     . 

75,080 
140,424 

131,700 
187,748 

177,624 

209,493 

230,392 
391,422 

278,718 
528,542 

Georgia  

1,057,280 

1,184,109 

1,542,180 

1,837,353 

2,210,331 

Hawaii   

154,001 

Idaho      
Illinois    .... 

1,711,951 

14,999 
2,539,891 

32,610 
3,077,871 

84,385 
3,826,351 

161,772 
4,821,550 

Indiana  

1,350,428 

1,680,637 

1,978,301 

2,192,404 

2,516,462 

Indian  Territory  .... 
Iowa 

674  913 

1,194  020 

1  624  615 

179,321 
1,911,896 

392,060 
•2  231,853 

Kansas              ... 

107  200 

364,31)9 

990  090 

1,427,090 

1,470,495 

Kentucky    
Louisiana    
Maine     
Maryland    
Massachusetts  
Michigan     
Minnesota   
Mississippi 

1,155,084 
708,01)2 
628,279 
687,049 
1,231,060 
749,113 
172,023 
791,30") 

1,321,011 
726,915 
620,915 
780,894 
1,457,351 
1,184,059 
439,700 
827,922 

1,048,690 
939,940 
648,936 
934,943 
1,783,085 
1,636,937 
780,773 
1,131  597 

1,858,035 
1,118,587 
661,086 
1,042,390 
2,238,943 
2,093,889 
1,301,826 
1,289  600 

2,147,174 

1,381,025 
694,400 
1,188,044 
2,805,346 
2,420,982 
1,751,394 
1,551  270 

Missouri      .          .          . 

1,182,012 

1,721,295 

2,168,380 

2,679,184 

3,106,605 

Montana 

20  595 

39  159 

132  159 

243  329 

Nebraska     
Nevada 

28,841 
6  857 

122,993 
42  491 

452,402 
62  '>()() 

1,058,910 
45  761 

1,060,300 
42  335 

New  Hampshire   .... 
New  Jersey      

320,073 
672,035 

318,300 
900,096 

340,991 
1,131  110 

370,530 
1  444  <)33 

411,588 
1,883  009 

New  Mexico     
New  York   j 
North  Carolina     .... 
North  Dakota 

93,516 
3,880,735 
992,622 

91,874 
4,382,759 
1,071,361 

119,505 
5,082,871 
1,399,750 

153.593 
5,997,853 
1,617,947 
182  719 

195,310 

7,208,894 
1,893,810 
319  146 

Ohio  

2,339,511 

2  665,260 

3  198,062 

3,672  316 

4,157,545 

Oklahoma 

61  834 

398  331 

Oregon 

52  465 

90  923 

174  768 

313,767 

413,536 

Pennsylvania  ... 

2  906  215 

3  521  951 

4  282,891 

5,258,014 

6,302,115 

Rhode  Island  
South  Carolina     .... 
South  Dakota  
Tennessee    . 

174,620 

703,708 

1  109  801 

217,353 
705,606 

1  258  520 

276,531 
995,577 

1,542,359 

345,500 
1,151.149 

328,808 
1,767,518 

428,556 
1,340,316 
401,570 
2,020,616 

Texas      

604  215 

818,579 

1,591,749 

2,235,523 

3,048,710 

Utah  
Vermont     
Virginia  . 

40,273 
315,098 
1,590,318 

86,786 
330,551 
1,225,163 

143,963 

332,286 
1,512,565 

207,905 
332,422 

1,655,980 

276,749 
343,641 

1,854,184 

Washington     
West  Virginia  
Wisconsin        .          ... 

11,594 

775,881 

23,955 
442,014 
1,054,670 

75,116 
618,457 
1,315,497 

349,390 
762,704 

1,686,880 

518,103 
958,800 
2,069,042 

Wyoming    

9,118 

20,789 

60,705 

92,531 

Total  .     . 

ADDITION  29 

7.  Arrange  the  following  data  in  tabular  form,  in  six  columns. 
Add  by  columns  and  by  lines  and  check  the  work  by  finding 
the  sum  of  the  vertical  and  horizontal  totals. 

The  attendance  at  a  state  fair  for  a  week  was  as  follows : 
Monday:  officials,  384  ;  other  adults,  4162  ;  children,  875 ;  single 
carriages,  489 ;  double  carriages,  164.  Tuesday:  officials,  437  ; 
other  adults,  5286  ;  children,  374  ;  single  carriages,  315  ;  double 
carriages,  100.  Wednesday:  officials,  311;  other  adults,  11,438; 
children,  986;  single  carriages,  721;  double  carriages,  209. 
Thursday:  officials,  280 ;  other  adults,  21,865 ;  children,  8219; 
single  carriages,  914  ;  double  carriages,  286.  Friday:  officials, 
118;  other  adults,  8211;  children,  452;  single  carriages,  136; 
double  carriages,  59.  Saturday:  officials,  118;  other  adults, 
9164;  children,  762  ;  single  carriages,  148  ;  double  carriages,  56. 

8.  Arrange  in  tabular  form,  in  seven  columns,  with  proper 
headings,  the  following  data.    Show  («)  the  total  departmental 
sales,  (6)  the  total  monthly  sales,  and  (c)  the  total  yearly  sales. 
Check  the  results. 

The  sales  of  E.  H.  Robinson  &  Co.  for  the  year  ending  June 
30,1908,  were  as  follows:  July,  1907:  books,  14162.18;  shoes, 
89162.17;  millinery,  15218.19;  dry  goods,  827,162.50;  gloves, 
82816.49;  furniture,  89267.50.  August:  books,  82160.59; 
shoes,  84162.87;  millinery,  86714.92;  dry  goods,  828,146.92; 
gloves,  81624.80;  furniture,  87247.95.  September:  books, 
86216.45  ;  shoes,  84167.95;  millinery,  83142.89;  dry  goods, 
824,167.46  ;  gloves,  82140.17  ;  furniture,  88175.96.  October  : 
books,  82786.90;  shoes,  84562.18;  millinery,  83147.98;  dry 
goods,  822,162.49;  gloves,  82478.67;  furniture,  88692.14. 
November:  books,  84675.82;  shoes,  84864.19;  millinery, 
86416.90;  dry  goods,  824,160.92;  gloves,  82841.16;  fur- 
niture, 8  641 8. 46.  December:  books,  88746.90;  shoes,  84621.19; 
millinery,  85162.19;  dry  goods,  827,127.46  ;  gloves,  84846.19; 
furniture,  810,614.92.  January,  1908  :  books,  84641.19;  shoes, 
82462.18;  millinery,  84018.60  ;  dry  goods,  828,562.14  ;  gloves, 
82417.90;  furniture,  88642.14.  February:  books,  82418.64 ; 
shoes,  84267.32s  millinery,  83742.24;  dry  goods,  822,140.86; 


30  PRACTICAL   BUSINESS   ARITHMETIC 

gloves,  12019.30;  furniture,  $4867. 32.  March:  books,  $ 4416.95; 
shoes,  18618.94;  millinery,  $8437.46;  dry  goods,  $24,162.18; 
gloves,  $2814.92;  furniture,  $7596.54.  April:  books,  $2486.14  ; 
shoes,  $2876.90;  millinery,  $3249.84;  dry  goods,  $22,172.14 ; 
gloves,  $1865.92;  furniture,  $8714.95.  May:  books,  $2834.16; 
shoes,  $3547.24;  millinery,  $4214.90;  dry  goods,  $28,137.56; 
gloves,  $2272.18;  furniture,  $8416.59.  June:  books,  $2816.32; 
shoes,  $4756.19;  millinery,  $3952.84  ;  dry  goods,  $24,167.49; 
gloves,  $2467.14;  furniture,  $8619.42. 

9.  Arrange  the  following  data  in  tabular  form,  in  nine 
columns,  with  proper  headings.  Find  the  amount  of  milk  de- 
livered by  each  patron,  the  amount  received  at  the  creamery 
each  day,  and  the  amount  received  during  the  week.  Check. 

There  was  received  at  a  creamery,  during  the  first  week 
of  June,  milk  as  follows:  Sunday  :  from  C.  D.  Allen,  415 Ib. ; 
L.  B.  Brown,  695  Ib. ;  W.  D.  Carroll,  425  Ib. ;  J.  H.  Dean, 
165  Ib.;  F.  A.  Ellis,  726  Ib.;  J.  L.  Frey,  920  Ib.;  I.  T.  Good, 
214  Ib.;  E.  H.  Lord,  170  Ib.  Monday:  from  C.  D.  Allen, 
416  Ib.;  L.  B.  Brown,  702  Ib.;  W.  D.  Carroll,  426  Ib. ;  J.  H. 
Dean,  175  Ib.;  F.  A.  Ellis,  729  Ib.;  J.  L.  Frey,  964  Ib.;  L  T. 
Good,  216  Ib. ;  E.  H.  Lord,  172  Ib.  Tuesday  :  from  C.  D.  Allen, 
420  Ib.;  L.  B.  Brown,  711  Ib. ;  W.  D.  Carroll,  419  Ib.;  J.  H. 
Dean,  186  Ib. ;  F.  A.  Ellis,  728  Ib. ;  J.  L.  Frey,  963  Ib.;  I.  T. 
Good,  218  Ib.;  E.  H.  Lord,  174  Ib.  Wednesday  :  from  C.  D. 
Allen,  432  Ib.;  L.  B.  Brown,  709  Ib.;  W.  D.  Carroll,  430  Ib.; 
J.  H.  Dean,  176  Ib. ;  F.  A.  Ellis,  724  Ib. ;  J.  L.  Frey,  962  Ib.; 
I.  T.  Good,  217  Ib.;  E.  H.  Lord,  178  Ib.  Thursday  :  from  C. 
D.  Allen,  428  Ib.;  L.  B.  Brown,  709  Ib. ;  W.  D.  Carroll,  427  Ib. ; 
J.  H.  Dean,  178  Ib.;  F.  A.  Ellis,  729  Ib. ;  J.  L.  Frey,  966  Ib. ; 
I.  T.  Good,  217  Ib.;  E.  H.  Lord,  173  Ib.  Friday:  from  C.  D. 
Allen,  432  Ib.;  L.  B.  Brown,  700  Ib.;  W.  D.  Carroll,  420  Ib.; 
J.  H.  Dean,  170  Ib.;  F.  A.  Ellis,  746  Ib.;  J.  L.  Frey,  980  Ib.; 
I.  T.  Good,  246  Ib. ;  E.  H.  Lord,  170  Ib.  Saturday:  from  C. 
D.  Allen,  450  Ib.;  L.  B.  Brown,  721  Ib. ;  W.  D.  Carroll,  417  Ib. ; 
J.  H.  Dean,  178  Ib.;  F.  A.  Ellis,  740  Ib. ;  J.  L.  Frey,  920  Ib.; 
L  T.  Good,  314  Ib.;  E.  H.  Lord,  180  Ib. 


CHAPTER   V 

SUBTRACTION 
ORAL   EXERCISE 

State  the  number  that,  added  to  the  smaller  number,  makes  the 
larger  one  in  each  of  the  following: 

1.  344567889999887 
1213233^23164412 

2.  12    11     12    11    12    11    12    11    10    11    10    11    10    12    10 

9239834847    _64_75_3 

3.  18    17    16    17    16    15    14    15    14    13    13    16    15    14    13 

_9   _8jr_9_8_6j)jrjB_!_I_^_?j>j) 

4.  13    14    14    15    16    17    18    18    19    19    19    19    18    18    17 
11121113^213131213111614141X12 

5.  22    21    22    21    22    21    22    21    20    21    20    21    20    22    20 
191213191813141814171614171513 

6.  38    27    26    37    26    35    44    25    34    53    43    36    45    54    73 
291817291826391728443729384569 

7.  42    51    72    81    92    71    32    41    70    61    90    81    30    62    50 
3942637988632438645786742755£7 

47.    A  parenthesis  (  )  signifies   that  the  numbers  included 
within  it  are  to  be  considered  together.     A  vinculum  has 

the  same  signification  as  a  parenthesis. 


Thus,  15  -  (4  +  2),  or  15  -  4  +  2  signifies  that  the  sum  of  4  and  2  is  to 
be  subtracted  from  15. 

31 


32  PRACTICAL   BUSINESS   ARITHMETIC 

48.    Examples.    1.    Find  the  difference  between  849  and  162. 

SOLUTION.    2  from  9  leaves  7.     6  cannot  be  subtracted  from  4,  but  6 
>m  14  leaves  8.    Since  1  of  the  8  hundreds 
7  hundreds  remaining.     1  from  7  leaves  6. 


from  14  leaves  8.    Since  1  of  the  8  hundreds  has  been  taken,  there  are  but        •  /»Q 


CHECK.     687  +  162  =  849.  687 

The  above  is  a  common  method  of  subtraction.  For  practical  computation, 
however,  the  "making  change"  method  is  best.  It  is  easily  understood  and 
is  much  more  rapid  when  once  learned.  The  "making  change"  method  is 
illustrated  in  the  following  example  and  solution. 

2.    Find  the  difference  between  7246  and  4824. 

SOLUTION.     Think    "4  +  2=6,"  and  write   2;    "2  +  2  =  4,"  and       7246 

write  2  ;  "  8  +  4  =  12,"  and  write  4  ;  "  1  and  4x2=  7,"  and  write  2.      4824 

CHECK.    2422  +  4824  =  7246.  ~2422 

ORAL  EXERCISE 

1.  16 +23+?  =  54?  7.   16+18  +  16  =  25  +  ? 

2.  27  +  14  +  ?=72?  8.   72  +  17  +  11  =  37  +  ? 

3.  17 +  36  +  ?  =62?  9.    14  +  18  +  38  =  42  +  ? 

4.  19 +  17 +  12  +  ?  =57?  10.   12 +  16 +  12 +  14+?  =  75? 

5.  25 +  14 +  11  +  ?  =  75?  11.    16 +  15 +  19 +  15+?  =  93? 

6.  18  +  17  +  16  +  ?  =  70?  12.   18 +  17 +  15+ 29+?  =  98? 

WRITTEN  EXERCISE 

l.  Without  copying  the  individual  problems,  find  quickly 
the  sum  of  the  twenty  differences  in  the  following: 


$2140.50 
714.23 

84157.50 
1236.80 

85000.24 
249.17 

89000.72 
1246.18 

81379.54 
923.18 

83145.62 
2000.79 

81742.18 
842.16 

84756.83 
2738.44 

85500.89 
2799.14 

81624.14 

957.80 

81985.72 
645.92 

89275.17 
842.99 

82446.80 
1321.44 

83169.14 

874.36 

83156.19 
1400.72 

88721.13 

2049.79 

87514.85 
721.92 

87291.80 
1642.95 

81756.92 
921.74 

81872.14 
742.12 

SUBTRACTION 


33 


2.  Copy  the  following  table  and  show  (a)  the  total  exports 
for  each  year  given;  (5)  the  excess  of  exports  for  each  year 
given;  (e)  the  total  exports  and  imports  for  the  eleven  years; 
(cT)  the  total  excess  of  exports  for  the  eleven  years.  Check. 

IMPORTS  AND  EXPORTS  IN  THE  UNITED  STATES  FOR  TEN  YEARS 


YEAR  ENDING 

EXPORTS 

TOTAL 

EXCESS  or 

JUNE   30 

Domestic 

Foreign 

EXPORTS 

EXPORTS 

1895 

$793,392,599 

$14,145,566 

$731,969,965 

1896 

903,200,487 

19,406,451 

779,724,674 

1897 

1,032,007,603 

18,985,953 

764,730,412 

1898 

1,210,291,913 

21,190,417 

616,050,654 

1899 

1,203,931,222 

23,092,080 

697,148,489 

1900 

1,370,763,571 

23,719,511 

849,941,184 

1901 

1,460,462,806 

27,302,185 

823,172,165 

1902 

1,355,481,861 

26,237,540 

903,320,948 

1903 

1,392,231,302 

27,910,377 

1,025,719,237 

1904 

1,491,744,641 

25,910,377 

991,090,978 

1905 

1,491,744,641 

26,817,025 

1,117,513,071 

Total 

49.  The  common  method  of  making  change  is  to  add  to  the 
price  of  the  goods  purchased  a  sum  that  will  equal  the  amount 
offered  in  payment. 

Thus,  if  a  person  buys  groceries  amounting  to  74^  and  tenders  $1  in 
payment,  the  mental  process  of  the  clerk  in  making  the  change  is  as  follows: 
"74^  +  1^  +  25^  =  $!";  the  customer  should  receive  as  change  a  1-cent, 
piece  and  a  quarter  of  a  dollar. 

Obviously,  the  change  may  usually  be  made  in  a  number  of  ways.  In 
the  above  example  two  dimes  and  a  5-cent  piece  might  be  given  instead  of 
the  quarter  of  a  dollar.  But,  as  the  different  bills  and  coins  are  usually 
sorted  in  the  till,  the  experienced  clerk  generally  makes  change  in  the  sim- 
plest way ;  that  is,  with  the  largest  possible  denominations.  In  the  follow- 
ing exercise  name  the  largest  coins  and  bills  that  could  be  used. 


ORAL   EXERCISE 


1.    Name  the  coins  and  the  amount  of  change  to  be  given 
from  $1  for  each  of  the  following  purchases  :   17  ^  ;   24  ^ ;   31  $  \ 

38^;  45^;   52^;    59^;    66^;    73^;    80^;    87^;  180; 
29^;  46^;   53  ^j  60^;   67^;    74^;   81^;   88  £ 


34  PRACTICAL   BUSINESS   ARITHMETIC 

2.  Name  the  coins  and  the  amount  of  change  to  be  given 
from  |2  for  each  of  the  following  purchases:  $1.19;  $1.26; 

$1.33;  $1.40;  $1.47;  $1.54;  $1.61;  $1.68;  $1.75;  $1.82; 
$1.89;  $1.20;  $1.27;  $1.34;  $1.41;  $1.48;  $1.55;  $1.62; 
$1.69;  $1.76;  $1.83;  $1.90. 

3.  Name  the  bills  and  coins  and  the  amount  of  change  to  be 
given  from  $5  for  eacli  of   the  following   purchases:    $1.21; 
$1.28;  $1.35;  $1.42;   $2.22;    $2.29;   $2.36;   $4.43;   $3.49; 
$4.50;   $3.51;  $3.56;   $4.57;   $2.58;   $1.63;   $2.64;   $1.65; 
$1.70;   $2.71;  $3.72;   $2.77;   $3.84;   $1.91;   $2.85;   $2.92. 

4.  Name  the  bills  and  coins  and  the  amount  of  change  to  be 
given  from  $10  for  each  of  the  following  purchases:   $4.93; 
$3.86;  $7.70;  $2.44;   $8.37;   $5.30;   $3.23;    $5.17;   $4.24; 
$3.31;  $8.38;  $2.45;   $6.52;   $4.59;   $3.66;   $5.73;   $4.80; 
$3.87;  $2.88;  $7.81;   $9.74;   $5.67;   $3.60;   $4.53;   $2.46; 
$3.29;  $8.32;  $7.25;  $2.18;   $7.49;   $9.42;   $3.67;   $1.93. 

50.  It  is  frequently  necessary  to  find  the  difference  between 
a  minuend  and  several  subtrahends.     If  the  "  making  change  " 
method  of  subtraction  is  employed,  the  operation  is  a  simple 
one. 

51.  Example.    From  a  farm  of  578  A.  I  sold  at  one  time  162 
A.,  at  another  98  A.,  and  at  another  121  A.     How  many  acres 
remained  unsold  ? 

f  rr  Q      * 

SOLUTION.     Arrange  the  numbers  as  shown   in. the   margin.  °'°  A* 

Eleven  (1  +  8  +  2)  and  seven  are  18  ;  write  7.     Three  (1  carried  162  A. 

+  2),  eighteen  (3  +  9  +  6)  and  nine  are  twenty-seven;  write  9.  93 

Four  (2  carried  +1  +  1)  and  one  are  5  ;  write  1.  -.9-1 

CHECK.     197  +  121  +  98  +  162  =  578.  -^- 

197  A. 

WRITTEN   EXERCISE 

Find  the  amount  each  person  has  remaining  on  deposit: 

1.  A.    Deposit,  $900;  checks,  $210,  $175,  $198. 

2.  B.    Deposit,  $875;  checks,  $157,  $218,  $157. 

3.  C.    Deposit,  $750;   checks,  $120,  $117,  $121,  $118. 

4.  D.    Deposit,  $960;  checks,  $128,  $109,  $118,  $117. 


SUBTRACTION 


35 


5.  E.    Deposit,  8967;  checks,  8192,  8102,  8117,  8128,8146. 

6.  F.    Deposit,  8998  ;  checks,  8 119,  8117,  8105,  8123, 8173. 

Do  not  neglect  to  check  all  work.  The  bank  clerk  who  makes  an  error 
a  day  in  work  like  the  above,  and  who  fails  to  discover  and  correct  this 
error,  will  not  long  retain  his  position. 

7.  Copy  the    following,    supplying   the    missing   terms    and 
checking  the  results  : 

8148.90  +  8149.75  +  8421.77  =  $???.?? 
118.60+  172.12+  ???.??=  ???.?? 
242.30+  ???.??+  210.96=  ???.?? 
???.??+  168.72  +  130.41  =  ???.?? 

8718.95  +  8698.75  +  8978.60  =  8??  ?  ?.  ?  ? 

The  following  problem  shows  a  portion  of  a  bank  discount  register.  In 
the  first  column  are  recorded  the  amounts  of  several  notes  that  have  been  dis- 
counted ;  in  the  second,  the  discount  charges;  and  in  the  third,  the  collection 
and  exchange  charges.  The  proceeds  of  any  note  is  the  difference  between 
the  amount  (face)  of  the  note  and  the  total  charges  upon  it. 

8.  Copy  and  complete  the  following  bank  record.      Check 
the  work.      (/  +  i  +  h  should  equal  #.) 


FACE  OF  PAPER 

DISCOUNT 

COLL.  &  EXCH. 

PROCEEDS 

729 

14 

7 

29 

73 

a 

862 

29 

4 

31 

86 

b 

725 

74 

7 

26 

73 

c 

832 

16 

12 

48 

1 

26 

d 

426 

19 

6 

39 

43 

e 

378 

36 

8 

78 

38 

f 

9 

k 

I 

j 

52.  The  complement  of  a  number  is  the  difference  between 
the  number  and  a  unit  of  the  next  higher  order. 

Thus,  2  is  the  complement  of  8,  23  is  the  complement  of  77,  and  152  is 
the  complement  of  848.  3  and  7,  24  and  76,  250  and  750,  are  complementary 
numbers.  Observe  that  ichen  tivo  numbers  of  more  than  one  figure  each  are 
complementary,  the  sum  of  the  units'  figure  is  10  and  the  sum  of  the  figures  in 
each  corresponding  higher  order  is  9. 


36  PEACTICAL   BUSINESS   ARITHMETIC 

53.  Since  numbers  are  read  from  left  to  right,  in  finding  the 
complement  of  a  number,  begin  at  the  left  to  subtract. 

54.  In   beginning  at  the  left  to  subtract  take  1  from  the 
highest  order  in  the  minuend  and  regard  the  other  orders  as 
9's,  except  the  last,  which  regard  as  10. 

55.  Example.    A  man  gave  a  100-dollar  bill  in  payment  for 
an  account  of  $77.52.     How  much  change  should  he  receive  ? 

SOLUTIONS,  (a)  Begin  at  the  left.  7  from  9  leaves  2;  7  from  9  $100.00 
leaves  2  ;  5  from  9  leaves  4;  2  from  10  leaves  8.  Or  «y  r9 

(6)   7  and  2  are  9 ;  7  and  2  are  9  ;   5  and  4  are  9  ;  2  and  8  are 
10.     $22.48. 

This  method  of  finding  the  amount  of  change  is  used  by  many  clerks  and 
cashiers.  The  work  is  in  all  cases  proved  by  counting  out  to  the  customer 
the  bills  and  coins  necessary  to  make  the  amount  of  the  purchase  equal  to 
the  amount  offered  in  payment. 

ORAL  EXERCISE 

State  the  difference  between  the  following  amounts  : 

1.  $1.00    11.00    $1.00    $1.00    $1.00    $1.00    $1.00     $1.00 

.22        .29        .36        .85        .78         .64       _.57         .56 

2.  $1.00    $2.00    $3.00    $4.00    $5.00    $6.00    $7.00     $8.00 

.54      1.36      2.02      2.17      2.23      5.01       5.23       7.21 

3.  $10.00  $10.00  $10.00  $10.00  $10.00  $10.00  $10.00  $10.00 

8.75      5.63      4.68      5.35      2.38      2.89      1.51       8.35 

4.  $50.00  $50.00  $50.00  $50.00  $50.00  $50.00  $50.00  $50.00 

28.14     17.49     11.52     16.84     14.89     12.52     19.64     21.87 

5.  If  $100  is  offered  in  payment  for  each  of  the  following 
bills,    what  amount  of  change  should  be  returned?     $27.42; 
$89.17;  $64.11;  $53.41;  $18.75;  $23.14;  $37.48;  $87.37. 

6.  If  $20  is  offered  in  payment  for  each  of  the  following 
bills,   what    amount  of    change  should  be   returned?     $4.72; 
$8.17;  $19.21;  $17.41;  $2.46;  $17.48;  $11.42 ;  $7.43;  $12.64; 
$11.42;  $4.96;  $1.16;  $7.25;  $15.98;  $16.87;  $14.17;  $13.56. 


SUBTRACTION  37 

ORAL  EXERCISE 

State  the  amount  of  change  in  each  of  the  following  problems : 

COST  OF  AMOUNT  COST  OF  AMOUNT 

ITEMS  PURCHASED       PAID  ITEMS  PURCHASED  PAID 

1.  17^,13^,42^  12  14.  $1.25,  $0.75,12.18  $20 

2.  27^,23^,14^  $2  is.  $1.50,  $2.70,  $1.18  $20 

3.  45^,  55  £  13^  $5  16.  $4.60,  $1.40,  $2.13  $20 

4.  64^,  16£  87^  $5  17.  $1.50,  $1.20,  $2.30  $10 

5.  23^,14^,27^  $2  is.  $3.17,  $4.11,  $4.98  $50 

6.  63^17^,59?  $5  19.  $4.25,  $0.75,  $3.18  $20 

7.  49^,  84^,  37^  $5  20.  $1.29,  $2.17,  $1.50  $20 

8.  78^,42^,67^  $5  21.  $1.64,  $1.66,  $2.50  $20 

9.  52^,  69^,  88^  $5  22.  $1.59,  $23.41,   $118  $200 

10.  75^,86^,54^  $5  23.  $24.17,  $20.83,     $15  $100 

11.  89^,  46^,  72^  $5  24.  111.48,  $10.52,     $50  $100 

12.  76^,54^,29^  $5  25.  $18.91,  $12.09,     $45  $100 

13.  75^,25^,89^  $10  26.  $21.27,  $2.73,  $50.50  $100 

56.  19  —  7  =  9  (the   minuend    minus  10)  +  3    (the  comple- 
ment of  the  subtrahend);  191  —  17  =  91  (the  minuend  minus 
100)  -+  83  (the  complement  of  the  subtrahend)  ;  1912  -  178  = 
912  (the  minuend  minus  1000)  +  822  (the  complement  of  the 
subtrahend),  and  so  on. 

57.  This  principle  makes  it  a  simple  matter  to  find  the  dif- 
ference between  a  subtrahend  and  several  minuends. 

58.  Examples.   The  following  examples  illustrate  the  appli- 
cation of  the  principle : 

SOLUTIONS.     1.    2  (the  complement  of  8),           i.  2.  3. 

10,  16;  16  — 10  =  6.  9  (the  complement  of  1),         QI«  OQQ  on 

HUTi  17-10  =  7.     9,  13,  16;  16-10=6.            J«  JJ 

2.  9,  17,  26;  26-10  =  16;  that  is,  6  and  1    +-±<O  +4^  +111 
to  add  to  the  minuends.    9,  18  (9+8  +  1),  27;    —118  -111  —219 
27-10  =  17;  that  is,  7  and  1  to  add  to  the    —(j'JQ  =676  =203 
minuends.     9,  14,  16;  16-10=6. 

3.  1,  2,  3.     3  —  10  is  impossible,  so  subtract  1  ten  from  the  minuend  (or  add 
1  ten  to  the  subtrahend).     9,  10.     10-10  =  0.     8,  9,  12.  12-10  =  2. 


38 


PRACTICAL   BUSINESS   ARITHMETIC 


59.   Example.    The  following  problem  shows  a  concrete  appli- 
cation of  the  foregoing  principle  : 


DEPOSITORS'  LEDGER 


DEPOSITOR 

BALANCE 

CHECKS 

DEPOSITS 

BALANCE 

A 

|74 

125 

$86 

$135 

B 

|86 

$11 

$99 

$174 

C 

$92 

$79 

$  81 

9    94 

SOLUTION.      Here   is  a 

depositors'  ledger.  The 
data  in  the  first  three 
columns  being  given,  it 
is  required  to  find  the 
new  balance. 

The  process  is  as  follows:    A.  6,  11,  15,  5;   8,  16,  23,  13;  balance,  ,$135. 

B.  9,  18,  24,  4  and  1  to  add  to  the  minuend.     10,   19,  27,  17;  balance,  $174. 

C.  1,  2,  4  and  1  to  take  away  from  the  minuend.     7,  10,  19,  9;  balance,  $94. 

WRITTEN  EXERCISE 

Find  the  neiv  balances,  the  total  old  balance,  the  total  checks,  the 
total  deposits,  the  total  new  balances,  and  check  the  work: 

1.  2. 


DEPOSITOR 

BAL. 

CllKCKS 

DEPOSITS 

BAL. 

A 

$758 

*  12S 

$  421 

a 

B 

921 

154 

175 

b 

C 

934 

214 

122 

c 

D 

862 

162 

218 

d 

E 

478 

187 

126 

e 

F 

921 

215 

124 

f 

G 

756 

157 

137 

<j 

H 

864 

128 

142 

h 

I 

926 

214 

121 

i 

J 

752 

221 

124 

J 

K 

878 

162 

218 

k 

/ 

m 

n 

o 

DEPOSITOU 

I5.U,. 

CHICKS 

DEPOSITS 

BAL. 

A 

$  428 

$125 

$  718 

a 

B 

726 

128 

296 

b 

C 

832 

279 

318 

c 

D 

456 

154 

421 

d 

E 

298 

275 

568 

e 

F 

728 

178 

188 

f 

G 

762 

218 

215 

9 

II 

837 

316 

176 

h 

I 

493 

121 

219 

i 

J 

862 

128 

188 

J 

K 

925 

125 

211 

k 

I 

m 

n 

0 

60.  48  —  29  =  48  +  1  (30,  the  next  higher  order  of  units  than 
29, -29) -30,  or  19;  128-59=128  +  1-60,  or  69. 

61.  This  principle  may  be  applied  to  advantage  in  billing 
items  in  which  the  gross  weights  and  the  tares  are  recorded. 

The  gross  weight  is  the  weight  of  merchandise,  together  with  bag,  cask, 
or  other  covering;  the  tare  is  the  weight  of  the  bag,  cask,  or  other  covering 


SUBTRACTION 


39 


of  merchandise ;  the  net  weight  is  the  difference  between  the  gross  weight 
and  the  tare. 

62.  Example.  The  gross  weights  and  tares,  in  pounds,  of  3 
bbl.  of  sugar  are:  332  -  19,  337  -  18  335  -  18.  Find  the  total 
net  weight. 

SOLUTION.     The  numbers 

would  be  written  on  the  bill  y4H# 

horizontally,  as  shown  in  the  margin.  Adding  the  units  of  the  tare,  the  result 
is  25  ;  30  (the  next  higher  order  of  units  than  25)  minus  25  equals  5  ;  5  added 
to  the  units  of  the  gross  weight  equals  19 ;  19  —  30  is  impossible,  so  write  9 
and  subtract  2  tens  (the  difference  between  the  tens  in  30  and  19)  from  the 
gross  weight  or  add  2  tens  to  the  tens  of  the  tare.  Adding  2  tens  to  the  tens 
of  the  tare,  the  result  is  5  ;  10  —  5  =  5  ;  5  added  to  the  tens  of  the  gross  weight 
equals  14  ;  14  —  10  =  4.  Adding  the  hundreds  in  the  gross  weight,  the  result 
is  9.  Net  weight  is  949  Ib. 

WRITTEN    EXERCISE 

Copy  the  following  bills.  Verify  the  net  weights  given  and  sup- 
ply all  missing  terms. 

1. 


Terms 


Bought  of  PHILIP  ARMOUR  &  CO. 


2.3 


JUL 


PKACTICAL   BUSINESS   ARITHMETIC 


Chicago,  111.,       July  20,       19 

Messrs.   A.   M.    THOMPSON  &  CO. 

Rochester,   N.Y. 

of  Nelson,  Morris  &  Co 


Terms   50   days 


6 

tubs  Lard 

72-17  70-14 

69-14  71-14 

71-15  70-16      ***  $0.11 

36 

63 

6 

casks  Shoulders 

421-65  426-70 

424-72  422-64 

427-72  421-60   ****    .12 

256 

56 

6 

casks  Hams 

409-72  412-70 

414-71  410-73 

412-70  416-71   ****    .12 

245 

52 

*** 

** 

3.  The  gross  weights  and  tares  of  6  casks  of  shoulders  are 
as  follows:   428-68,  419-70,  423-65,  432-72,  436-69, 
434  —  65  Ib.     Find  the  total  net  weight. 

4.  The  gross  weight  and  tares  of  12  tubs  of  lard  are  as  fol- 
lows :    71-14,    70-15,    69-14,    71-15,   72-17,    73-17, 
69-15,  71-16,  72-15,  73-16,  74-17,  75-17  Ib.     Find 
the  total  net  weight. 

5.  The    gross  weights  and  tares  of  10  bbl.  of  sugar  are  as 
follows:     319-18,    331-19,    329-17,    334-20,    338-21, 
325  -  18,   326  -  16,  325  -  19,  327  -  19,  321  -  17  Ib.     Find  the 
total  net  weight. 


SUBTRACTION 


41 


BUSINESS   TEEMS   AND   RECORDS' 

63.  A  debit  is  an  expression  of  value  received ;    a  credit  is 
an  expression  of  value  delivered. 

A  buys  of  B  100  bu.  wheat  for  $100  cash;  the  value  received  (debit) 
by  A  is  100  bu.  wheat  and  the  value  parted  with  (credit),  $100.  A  sells  C 
50  bu.  wheat  for  $75,  C  agreeing  to  pay  for  the  same  in  10  da. ;  the  value 
received  by  A  is  C's  express  or  implied  promise  to  pay  for  the  wheat  in  10  da. 
and  the  value  parted  with  is  50  l>u.  wheat. 

64.  An  account  is  a  collection  of  related  debits  and  credits. 

65.  Some  of  the  common  accounts  kept  in  business  are  the  cash 
account ;    personal  accounts ;    the  merchandise   account ;    the 
expense  account ;  the  proprietary  account. 

66.  A  resource  is  any  property  on  hand  or  any  amount  owed 
to  a  person  or  concern;  a  liability  is  any  amount  owed  by  a 
person  or  concern.     The  excess  of  resources  over  liabilities  is 
the  net  capital  or  present  worth ;  the  excess  of  liabilities  over 
resources,  the  net  insolvency. 

67.  A  gain  is  any  sum  realized  in  excess  of  the  cost  of  a 
business  or  of  business  transactions ;  a  loss  is  any  sum  spent 
or  incurred  in  excess  of  the  returns  of  a  business  or  of  business 
transactions.     The  excess  of  gains  over  losses  is  the  net  gain ; 
the  excess  of  losses  over  gains,  the  net  loss. 

68.  The  cash  account  is  kept  for  the  purpose  of  showing  the 
receipts  and  payments  of  cash  and  the  amount  of  cash  on  hand. 


The  receipts  of  cash  are  entered  on  the  left  or  debit  side,  and  the  pay- 
ments, on  the  right  or  credit  side,  of  the  account.  The  excess  of  debits  at 
any  time  is  the  amount  of  cash  on  hand. 


42 


PRACTICAL   BUSINESS   ARITHMETIC 


69.  Personal  accounts  are  kept  for  the  purpose  of  showing 
whether  persons  owe  us  or  we  owe  them,  and  how  much  in 
either  case. 


On  the  left  (debit)  side  of  these  accounts  are  placed  the  amounts  which 
the  persons  owe  us  or  which  we  pay  them  ;  on  the  right  (credit)  side,  the 
amounts  which  we  owe  them  or  which  they  pay  us.  When  the  debits 
of  an  account  are  in  excess  of  the  credits,  the  account  owes  us  for  the  amount 
of  the  excess;  when  the  credits  are  in  excess  of  the  debits,  we  owe  the  ac- 
count for  the  amount  of  the  excess. 

70.  The  merchandise  account  is  kept  for  the  purpose  of  show- 
ing the  cost  of  goods  purchased,  the  proceeds  of  goods  sold,  and 
the  gain  or  loss  resulting  from  such  dealings. 


/f 


/  60  7  e 
720 


On  the  left  (debit)  side  is  entered  the  cost  of  goods  purchased  and  on  the 
right  (credit)  side  the  proceeds  of  goods  sold.  When  the  goods  are  all 
disposed  of  the  excess  of  credits  is  a  gain  ;  the  excess  of  debits,  a  loss. 
When  it  is  desired  to  show  the  gain  or  loss  on  merchandise  before  the 
goods  are  all  disposed  of,  it  is  necessary  to  first  enter  in  the  credit  side  of 
the  account  the  present  market  value  of  the  unsold  goods. 


SUBTRACTION 


43 


71.   The  expense  account  is  kept  for  the  purpose  of  showing 
the  cost  of  outlays  incurred  in  carrying  on   the  business. 


2  0  <?# 


/  2  ^0 


/z 

J-J 30 


Such  outlays  are  entered  on  the  left  (debit)  side  of  the  account.  Ordi- 
narily there  are  no  credit  entries.  When  the  expense  items  are  all  used  the 
debit  of  the  account  is  a  loss.  When  it  is  desired  to  show  the  loss  or  gain 
on  expense  and  there  are  unused  expense  items  on  hand,  it  is  first  necessary 
to  enter  in  the  credit  side  of  the  account  the  present  value  of  such  items. 

72.  The  proprietary  account  is  kept  for  the  purpose  of  show- 
ing whether  the  proprietor  owes  the  business  or  whether  the 
business  owes  him,  and  how  much  in  either  case. 


J/ 


On  the  right  (credit)  side  are  entered  all  sums  invested  and  the  net  gain, 
and  on  the  left  (debit)  side  all  sums  withdrawn  and  the  net  loss.  The 
excess  of  credits  is  the  present  worth  of  the  business. 

ORAL  EXERCISE 

1.  In  the  cash  account  on  page  41  what  are  the  total  receipts? 
the  total  payments  ?  the  balance  of  cash  on  hand  ? 

2.  At   the    top    of   page   42    is   your    account   with    J.    E. 
King  &  Co.     On  what  dates  did  you  sell  the  firm  merchandise  ? 
When  and  how  were  payments  made  on  account  ?     What  was 
the  balance  of  the  account  May  10  ? 


44  PRACTICAL   BUSINESS   ARITHMETIC 

3.  In  the  account  with  merchandise,  page  42,  what  is  the 
cost  of  the  purchases?  the  proceeds  of  the  sales?     How  would 
the  value  of   the  unsold   goods    be    determined   in   business  ? 
Verify  the  amount  of  the  gain.     Is  it  correct  ? 

4.  Verify  the  amount  of  the  loss  in  the  expense  account, 
page  43.     Is  it  correct? 

5.  What   are   the   total   withdrawals   in   the    account    with 
F.  W.    Simpson,  Proprietor,  page   43  ?  the  total  investment  ? 

WRITTEN    EXERCISE 

1.  Copy  the  cash  account  on  page  41  and  continue  it  with 
the   following   items:  Jan.   12,   receive   cash  of   Jones  &  Co., 
$75;  Jan.  14,  pay  cash  for  groceries,  $165.62;  Jan.  15,  re- 
ceive cash  for  groceries,  1189.75  ;  Jan.    18,  pay  cash  to  office 
help,    $129.74;     Jan.   20,  pay    cash    for   stationery,    $11.75; 
Jan.  22,  receive  cash  for  groceries,  $126.94  ;  Jan.  24,  receive 
cash  of  H.  W.  Conant,  $200,67.     Balance  the  account  as  shown 
in  the  model. 

2.  Copy  the  purchases  and  sales  of  the  merchandise  account, 
page  42.      Assuming   that   the   value   of  the  unsold  goods  is 
$327.61,  find  the  gain  and  close  the  account. 

3.  Copy  the  purchases  and  sales  of  the  merchandise  account, 
page  42.      Assuming  that  the  value  of  the  unsold  goods  is  $50, 
find  the  gain  or  loss  and  close  the  account.     Assuming  that  all 
of  the  goods  are  sold,  find  the  gain  or  loss  and  close  the  account. 

4.  Arrange  the  following  data  in  the  form  of  your  account 
with    Benj.    F.    Butler.       June    1,  buy  of  Benj.  F.  Butler  on 
account  (without  making  payment)   dry  goods  amounting  to 
$627.96;   June  10,  pay  him   for  invoice  of  June   1  less  $6.28 
discount;   June  28,  buy  of  him  dry  goods  amounting  to  $472. 69 
and  pay  cash  to  apply  on  the  bill,  $172.69;  July  15,  buy  of  him 
on  account  dry  goods  amounting  to  $369.71;  July  31,   pay  him 
cash  to  apply  on  bill  of  July  15,  $79.79;  Aug.  2,  sell  him  lace 
amounting  to  $14.60.      Find  the  balance  of  the  account  and 
tell  whether  such  balance  is  a  resource  or  a  liability. 


SUBTRACTION 


45 


5.  Using  the  above  data,  write  Benj.  F.  Butler's  account  of 
his  dealings  with  you.     Balance  the  account. 

6.  Copy  the  account  with  F.  W.  Simpson,  Prop.,  page  43. 
Continue  the  account  through  June,  using  the  following  items : 
June  6,  make  an   additional    investment  of    §1000;    June  25, 
withdraw  for  personal  use  1160;  June  30,  the  net  gain  for  the 
month,   which    is   to    remain   as  an    additional  investment,   is 
$369.75.     Find  the  present  worth  and  close  the  account. 

ORAL  EXERCISE 

Classify  the  following  as  resources,  liabilities,  losses,  or  gains: 
1.    A  personal  account  showing  a  debit  balance  of  $150. 
2     A  personal  account  in  which  the  credit  balance  is  $270. 

3.  A  merchandise  account  in   which  there  are  no  goods  on 
hand  and  the  purchases  aggregate  $7160  and  the  sales,  $8249.50. 

4.  The  total  losses  of  a  business  are  $480,  and  the  net  gain, 
$  640.90.     What  are  the  total  gains  ? 

5.  The  total  liabilities  of  a  concern  are  $2400,  and  the  pres- 
ent worth,  $6280.50.     What  are  the  total  resources  ? 

WRITTEN   EXERCISE 
Copy  the  following  statements,  supplying  the  missing  terms: 


32.00 


•<?£.<?# 


46 


PRACTICAL   BUSINESS   ARITHMETIC 
2. 


3.  A  merchant  purchased  a  stock  of  hardware  amounting  to 
§45,112.18  and    sold    from    this    stock    goods   amounting   to 
$31,136.85.     He  then  took  an  account  of  stock  and  found  that 
the  value  of  the  hardware  on  hand  was  $  18,438.50.     Find  the 
amount  of  his  gain. 

4.  C.   E.   Cyr's    resources   and    liabilities   at  the  close  of  a 
month  were  as  follows:    dry  goods  on  hand,  $  1629.40;  store 
and  lot,  13000;  cash  in  bank,  11400.60;   C.  O.  Bond  owes  the 
business   1400;     L.    E.    Young,    1390.10;     and    J.    O,    Snow, 
$209.90..    The  business  owes  Roe  &  Co.  1750;  and  Doe  &  Co. 
$90.75.     Make  a  statement  of  resources  and  liabilities. 

5.  At  the  close  of  the    same    month  C.   E.   Cyr's   business 
accounts    show   the  following  results:    stock  of  dry  goods  on 
hand  at  the  beginning  of  the  month,  $1270.40;  purchases  of 
dry  goods  for  the  month,  $3229.60;  sales  of  dry  goods  for  the 
month,  $3762.90;   market  value  of  the  dry  goods  on  hand  at 
the    close    of  the   month,   $1629.40;    expense   for  the   month, 
$413.95;  value  of  expense  items  on  hand,  $250.     Make  a  state- 
ment of  losses  and  gains. 

6.  A    real    estate    agent  had    property  on    hand   Jan.   1   to 
the  amount  of  $8155.60.      During  the  year  he  bought  property 


SUBTRACTION  47 

costing  14150.60,  added  buildings  at  a  cost  of  16190.40,  and 
paid  taxes  §250.90.  April  15  a  house  valued  at  -11690  was 
destroyed  by  fire,  and  for  this  loss  the  insurance  company  paid 
him  $  1300.  During  the  year  he  sold  property  for  19260.50 
and  received  for  rents  §840.80.  If  the  expenses  of  the  sales 
aggregated  8240.19  and  the  value  of  the  property  on  hand 
Dec.  31  was  $11,250.60,  what  was  his  net  gain  or  loss  for 
the  year? 

73.  Banks  and  other  business 
houses  having  a  large  amount  of 
adding  to  do,  frequently  use  an  add- 
ing machine.  Because  it  cannot  be 
used  to  advantage  for  many  kinds  of 
addition,  this  machine  has  not  done 
away  with  the  necessity  for  the  hand- 
and-mind  method  of  addition  ;  on  the 
other  hand,  by  its  rapid  and  accurate  work,  it  has  put  a 
premium  on  the  hand-and-mind  method.  Business  men  will 
no  longer  tolerate  a  bookkeeper  who  is  slow  and  inaccurate  in 
his  additions  ;  but  the  person  who  can  add  with  speed,  accuracy, 
and  intelligence  is  more  than  ever  in  demand.  In  the  margin 
is  a  picture  of  an  adding  machine  such  as  is  commonly  used. 
The  operation  of  subtraction,  or  of  combined  addition  and  sub- 
traction, may  usually  be  performed  on  an  adding  machine. 

ORAL   REVIEW   EXERCISE 

1.  Find  the  sum  of  45,  45,  45,  45,  45,  and  60. 

2.  Find  the  sum  of  61,  62,  63,  64,  65,  66,  and  67. 

3.  Find  the  sum  of  102,  103,  104,  105,  106,  10T,  and  108. 

4.  Find  the  sum  of  all  the  integers  from  6  to  12,  inclusive. 

5.  How  many  days  from  Apr.   15  to  June  2?    from    Mar. 
15  to  May  3  ?  from  July  30  to  Sept.  5? 

6.  Count  backwards  rapidly  by   5's  from  96  ;  by    7's    from 
97 ;  by  13's  from  100  ;   by  12's  from  135 ;  by  14's  from  99. 

7.  Subtract   each    of    the    following    amounts     from    $50: 
124.19,  121.76,  $42.14,  $13.98,  $47.29,  $19.32,  $16.38,  $11.43. 


48  PRACTICAL   BUSINESS   AEITHMETIC 

8.    State  the  sum  of  each  of  the  following  groups: 

82?  79^  74^  52?  92^  38^  73^  69^  86?  63?  42?  26^  81?  27^ 
35?  18?  87^  31^  85^  57^  99?  34?  75?  28?  95^  19^  93^  41  ^ 


98?  46?  89?  72?  59^  30?  91?  80?  73?  53^  66^  24?  76? 
15^  45?  14?  88^  77^  97^  54^  78^  47^  62^  49^  32^ 


13^  90^  40^  96^  21^  84^  56^  58^  22^  48^  37^  50^ 
12^  94^  17^  83^  61^  65^  33^  44?  16^  70^  36?  51?  23? 


9.    State  the  difference  between  each  of  the  above  groups. 

In  subtracting  91  and  27  think  of  71  and  7,  or  64;  in  subtracting  52  and 
29  think  of  32  and  9,  or  23  ;  and  so  on. 

10.  State  the  difference  between  $  2  and  the  sura  in  each  of 
the  above  groups  ;  between  85  ;  between  $10. 

11.  What  change  should  I  receive  from  $2  if  I  spent: 
a.   26?  and  43??        e.    25?  and  37^?       i.    lo£  lM  and 
ft.   17?  and  59^?       /.    42^  and  39^?       j.    ll£  43?,  and 

c.  28?  and  52??       g.    19^  and  37??       k.    19?,  34?,  and  47?? 

d.  \lf  and  58^?       L    16^  and  29??        I    28^,  11^,  and  47?? 

12.  Add  each  of  the  following  numbers  to  each  of  the  num- 
bers below:  2,  8,  7,  6,  5,4,  9,  11,  12,  3,  14,  15,  16,  13,  18,  17,  19. 

First  add  by  lines  and  then  by  columns.  Thus,  to  add  7  by  lines  say  7, 
8,11,9,  12,  10,  13,  14,  17,  15,  18,  16,  19,  20,  and  so  on;  to  add  7  by  columns 
say  8,  20,  32,  44,  56,  68,  80,  92,  104,  116,  11,  and  so  on. 

abode    fgh    ij     kl 

1.  1   4   2   5   3   6   7   10   8   11   9   12 

2.  13  16  14  17  15  18  19  22  20  23  21  24 

3.  25  28  26  29  27  30  31  34  32  35  33  36 

4.  37  40  38  41  39  42  43  46  44  47  45  48 

5.  49  52  50  53  51  54  55  58  56  59  57  60 

6.  61  64  62  65  63  66  67  70  68  71  69  72 

7.  73  76  74  77  75  78  79  82  80  83  81  84 
a  85  88  86  89  87  90  91  94  92  95  93  96 
9.  97  100  98  101  99  102  103  106  104  107  105  108 

10.  109  112  110  113  111  114  115  118  116  119  117  120 


SUBTRACTION 


49 


WRITTEN   REVIEW  EXERCISE 

In  all  exercises  of  this  kind  a  time  limit  should  be  set  for  the  work.  The 
work  should  also  be  checked  before  answers  are  submitted  for  examination. 
Accuracy  is  of  paramount  importance  in  business.  One  error  that  passes 
unnoticed  by  the  student  in  ten  problems  of  this  character  is  a  failure. 

l.  Without  copying,  find  quickly  the  missing  terms  in  the 
following  statement  of  government  receipts  and  expenditures 
for  the  fiscal  year  closing  June  30  in  a  recent  year.  Check. 


From  customs 
Internal  revenue 
Miscellaneous 
Total 

Civil  and  miscellaneous 

War 

Navy 

Indians 

Pensions 

Interest 

Total 

Surplus 


RECEIPTS 


EXPENDITURES 


$262,068,483 

232,435,695 

46,682,565 


$132,229,913 
115,337,786 
102,757,073 

10,437,196 
142,558,335 

24,618,766 


2.    Without  copying,  find  the  totals  and  grand  totals  of  the 
following  table.     Check  the  results. 

COINAGE  OF  THE  MINTS  OF  THE  UNITED  STATES 


CALEXDAuYEAUt 

GOLD 

SILVER 

MINOR 

TOTALS 

1793  to  1894 
1895 

$1,732,552,32300 
59  616  357  50 

0681,909,71910 
5  698  010  25 

$25,391,53179 
882  430  56 

1896  
1897  
1898  

47,053,06000 
76,028,485  00 
77,985,757  50 

23,089,899  00 
18,487,297  30 
23,034,033  45 

832,71893 
1,526,10025 
1,124,835  14 

1899  

111,344,22000 

26,061,51990 

1,S37  451  86 

1900 

99  272  942  50 

36  295  321  45 

2  031  137  39 

1901   .  .  . 

101  735  187  50 

30  838  460  75 

2  120  122  08 

1902  

61,980,572  50 

30,116,36945 

2  4k>9  736  17 

1903  

45,721,77300 

25,996,536  25 

2  484,691  18 

1904  .    . 

233.402,428  00 

15,695,609  95 

1  683  529  35 

Grand  totals 

CHAPTER   VI 

MULTIPLICATION 
ORAL   EXERCISE 

1.  Which  of  the  following  numbers  are  concrete  ;  that  is,  re- 
fer to  some  particular  kind  of  object  or  measure  ?   12  ;   5^- ;  12 
ft.  ;   2.5  da.  ;   15  yd.  ;   18  men  ;   200;   $12  ;    172f 

2.  Which  of  the  above  numbers  are  abstract ;  that  is,  do  not 
refer  to  any  particular  kind  of  object  or  measure  ? 

3.  5  +  4  +  2  +  8  +  9  =  ? 

4.  9  +  9  +  9  +  9  +  9=?   5  times  9  =  ? 

5.  Could  the  sum  of  the  numbers  in  problem  3  be  found  by 
any  shorter  process  ? 

6.  What  is  the  first  process  in  problem  4  called  ?    the  second? 

7.  9  times  27  =  ?     9  times  29  bu.  =  ? 

8.  If  1  bu.  of  rye  weighs  56  lb.,  what  will  12  bu.  weigh? 

74.  Jn  problems  7  and  8  it  is  seen    that    the   multiplier   is 
always  an  abstract  number  ;  and  the  multiplicand  and  product  are 
like  numbers. 

75.  Three  5's  are  equal  to  five  3's  ;    1 3  multiplied  by  5  is 
equal  to  1 5  multiplied  by  3  ;  4  trees  multiplied  by  125  is  equal 
to  125  trees  multiplied  by  4. 

76.  It   is  therefore  seen  that  the  product  is  not  affected  by 
changing  the  order  of  the  factors  regarded  as  abstract  numbers. 

77.  The    multiplicand    and    multiplier   together   are    called 
factors  (makers)  of  the  product  ;   the  product  of  two  abstract 
integers  is  sometimes  called  a  multiple  of  either  of  the  factors. 

78.  Sometimes  a  number  is  used  several  times  as  a  factor. 
Numbers  so  used  are  indicated  by  a  small  figure,  called  an  expo- 
nent, written  above  and  at  the  right  of  the  factor. 

Thus,  4  used  twice  as  a  factor  is  written  42,  5  used  four  times  as  a  factor 
is  written  54,  and  6  used  Jive  times  as  a  factor  is  written  65. 

50 


MULTIPLICATION  51 

79.  The  product  arising  from  using  a  number  two  or  more 
times  as  a  factor  is  called  a  power  of  that  number. 

Thus,  4  is  the  second  power  of  2  ;  64  is  the  third  power  of  4  and  the  sixth 
power  of  2. 

Too  much  attention  should  not  be  given  to  the  definitions  like  the  above. 
They  are  valuable  only  as  they  help  to  make  clear  the  matter  in  the  exercises. 
They  are  rarely  heard  in  business  and  therefore  should  not  be  memorized. 

ORAL  EXERCISE 

1.  Multiply  at  sight  each  number  below  by  2 ;  by  3 ;  by  4  ; 
by  5 ;  by  6  ;  by  7  ;  by  8  ;  by  9. 

Name  the  products  by  lines  from  left  to  right  and  from  right  to  left; 
also  by  columns  from  left  to  right  and  from  right  to  left.  Name  results 
only.  Thus,  to  multiply  lines  by  4  say  20,  36,  8,  24,  40,  12,  28,  44,  16,  48, 
32,  52,  68, 84,  and  so  on  up  to  100 ;  and  backwards,  100,  80,  96,  64,  and  so  on 
back  to  20.  To  multiply  columns  by  4  say  20,  68,  36,  84,  and  so  on  to  52, 
100 ;  and  backwards  100,  52,  80,  32,  and  so  on  to  68,  20.  Continue  the  work 
until  results  can  be  named  at  the  rate  of  120  or  more  per  minute. 

5        9       2       6       10       3       7       11       4       12       8       13 
17       21     14     18       22     15     19       23     16       24     20       25 

2.  Multiply  as  instructed  in  problem  1  and  add  8  (carried) 
to  each  product.     Also  multiply  as  instructed  and  add  6,  4,  7, 
2,  5,  3,  and  9  to  each  product. 

Name  results  only.  Thus,  to  multiply  by  lines  say  20,28;  36,  44;  8, 
16  ;  and  so  on. 

3.  Multiply  by  2  :  27,  35,  81,  36,  28,  32,  47,  93,  56,  39,  54, 
45,  52,  86,  75,  67,  59.     Also  by  4,  3,  5,  8,  6,  7,  9. 

4.  Find  the  cost  of  each  of  the  following:   20  Ib.  crackers  at 
8^;   9  Ib.  coffee  at  34^;    7  Ib.  tea  at  57^;    11  Ib.  beef  at  \lf\ 
120  Ib.  sugar  at  4j*;  134  Ib.  sugar  at  5^. 

5.  Find  the  cost  of  each  of  the  following:  44  yd.  at  9^;  37 
yd.  at  8^;   123  yd.  at  6^;    214  yd.  at  4^;    52  yd.  at  12^;    29 
yd.  at  8^;  8yd.  at  $1.03;   7yd.  at  11. 01;  5  yd.  at  11.35. 

6.  Beginning  at  0  count  by  9's  to  81 ;  by  10's  to  150  ;  by  ll's 
to  154;   by  12's  to  108;   by  13's  to  117;  by  14's  to  126;  by 
15's  to  135 ;  by  16's  to  144 ;  by  17's  to  153 ;  by  18's  to  162 ;  by 
19's  to  171 ;  by  20's  to  180. 


52  PRACTICAL   BUSINESS   ARITHMETIC 

80.    Examples.    1.  Find  the  cost  of  2150  Ib.  at  5^. 

SOLUTION.     Since  1  Ib.  costs  5ft  2150  Ib.  will  cost  2150  times      $  21.50 
5^;  but  2150  times  5^    is  equal  to  5  times   2150ft    5    times  5 

$21.50  (2150^)  equals  $107.50,  the  required  result.  $  107.50 

2.    Multiply  224  by  46. 

SOLUTION.     In  multiplying  one  number  by  another,  224  224 

there  is  no  practical  advantage  in  beginning  with  the  46  46 

lowest  order  of  units  of  the  multiplier  ;   in  fact,  in  -»  ytt 


some  multiplications  (see  page  140)  there  is  a  decided  gQ«  1  Q_L1 

advantage  in  beginning  with  the  highest  order.  The 
arrangement  of  work  for  both  methods  is  shown  in 
the  margin. 

CHECK.  The  work  may  be  checked  by  multiplying  first  by  one  method  and 
then  by  the  other,  or  by  interchanging  the  multiplier  and  multiplicand  and  re- 
multiplying.  (See  also  pages  83  and  84.) 

3.    Multiply  2004  by  1275. 

SOLUTION.     When  one  of  two  numbers  to  be  mul-  1275  1275 

tiplied  contains  a  number  of  zeros  or  ones,  it  is  always  2004  2004 

easier  to  take  that  number  as  the  multiplier.     Since  vfOO 

the  product  of  any  number  multiplied  by  0  is  0,  the  9/rcn 

product  of  1275  multiplied  by  the  tens  and  hundreds  —  '-  -      - 

of  the  multiplier  need  not  be  written.  2555100      2555100 

CHECK.    The  problem  may  be  checked  the  same  as  problem  2. 

When  two  numbers  are  to  be  multiplied,  it  is  generally  easier  to  take  as 
the  multiplier  the  number  having  the  least  number  of  places.  Thus,  to  find 
the  cost  of  1647  A.  of  land  at  $27  per  acre,  take  27  as  the  multiplier. 

If  one  of  the  two  numbers  to  be  multiplied  has  two  or  more  digits  alike, 
it  is  easier  to  take  that  number  as  the  multiplier.  Thus,  to  multiply  to- 
gether 6729  and  7777,  it  is  easier  to  take  7777  as  the  multiplier. 

ORAL    EXERCISE 

1.  Find  the  value  of  51  T.  of  hay  at  $17  per  ton. 

2.  Find  the  cost  of  175  Ib.  of  sugar  at  5^  per  pound. 

3.  How  much  will  a  boy  earn  in  87  hr.  at  9^  an  hour? 

4.  What  is  the  cost  of  a  flock  of  52  sheep  at  1  7  per  head? 

5.  At  the  rate  of  47  mi.   an  hour,  how  far  will    a    person 
travel  in  12  hr.  ? 

6.  What  is  the  cost  of  12  pr.  of  shoes  at  $4.50  per  pair,   and 
8  pr.  of  boots  at  13.50  per  pair  ? 


MULTIPLICATION  53 

7.  What  must  be  paid  for  handling  12  loads  of  freight  at 
12.25  per  load? 

8.  In  an  orchard  there  are  13  rows  of  trees,  each  containing 
21  trees.     How  many  trees  in  the  orchard? 

9.  If  you  buy  5  pencils  at  9^  each  and  9  penholders  at  5^ 
each,  and  some  stationery  costing  25^,  how  much  change  should 
you  receive  from  a  two-dollar  bill?  from  a  ten-dollar  bill? 

10.  I  bought  6  cd.  of  wood  at  $5.75  per  cord.     If  a  fifty- 
dollar  bill  is  offered  in  payment,  how  much  change  should  be 
received? 

11.  I  bought  12  bu.  of  wheat  at  $1.05.     If  I  gave  in  pay- 
ment two  ten-dollar  bills,   what  change  should  I   receive? 

12.  My  average  marketing  expenses  per  day  are  $2.10.     If  I 
offer  a  twenty-dollar  bill  in  payment  for  7  days'  expenses,  what 
change  should  I  receive? 

13.  I  sold  16  chairs  at  $7  each,  and  5  tables  at  $9  each.     If 
two  one-hundred-dollar  bills  are  offered  in  payment,  how  much 
change  should  I  return?     If  a  one-hundred-dollar  bill,  a  fifty- 
dollar  bill,  and  a  twenty-dollar  bill  are  offered  in  payment,  how 
much  change  should  I  return? 

WRITTEN   EXERCISE 

In  the  following  problems  find  the  missing  numbers  by  multiply- 
ing across  and  adding  down.  Check  the  results  by  comparing  the 
sum  of  the  line  products  witli  the  sum  of  the  multiplicands  multi- 
plied by  one  of  the  multipliers. 

1.  2.  3. 

15x211=?  9x1475=?  12x116.50=? 

15x346=?  9x2618=?  12x127.75=? 

15x318=?  9x1575=?  12x114.95=? 

15x721=?  9x1792=?  12x829.86=? 

15x936=?  9x4936=?  12x$49.88=? 

15x849=?  9x7289=?  12x139.62=? 

15x21^=_?_  9x8728=_?^  12x186.99=  ? 

15  x    ?    =  ?  9  x     ?     =  ?  12  x       ?      =  ? 


54  PRACTICAL   BUSINESS   ARITHMETIC 

4.  5.  6. 

12x192=?  98x2178=?  16  x  $18.10=? 

12x721=?  98x1692=?  16  x    17.20=? 

12x836=?  98x2536=?  16  x    21.40=? 

12x456  =  ^_  98  x  2892  =  ?  16  x    25.85=  ? 

12  x    ?    =  ?  98  x     ?     =  ?  16  x       ?      =  ? 

Problems  such  as  the  above  are  very  helpful.  They  afford  a  variety  of 
work  and  suggest  a  simple  method  by  which  the  student  may  test  the  cor- 
rectness of  his  results.  The  teacher  should  add  as  many  more  problems  as 
circumstances  require. 

7.  A  produce  dealer  bought  2145  bu.  of  potatoes  at  23  ^  a 
bushel,  and  sold  them  at  47^  a  bushel.     What  did  he  gain? 

8.  A  drover  bought  125  head  of  cattle  at  115.75  per  head. 
He  sold  65  head  at  123.40,  15  head  at  $13.75,  and  45  head  at 
$17.75.     Did  he  gain  or  lose,  and  how  much? 

9.  A  grocer  bought  14  bu.  of  apples  at  35^  per  bushel  and 
12  bu.  of  potatoes  at  37^  per  bushel.     He  sold  the  apples  at  30 # 
a  peck  and  the  potatoes  at  20^  a  peck.     What  did  he  gain? 

10.  A  speculator  bought  1247  bbl.  of  apples  at  $1.35  per 
barrel.     After  holding  them  for  three  months  he  sold  them  at 
$3.75  per  barrel.     If  he  paid  $74.82  for  storage,  and  his  loss 
by  decay  was  equal  to  37  bbl.  of  apples,  what  was  his  gain? 

11.  The  gross  weight  in  pounds,  and  tare  in  pounds,  of  25 
tubs  of  lard  are  as  follows  :  71  -  14,  70  -  15,  69  -  14,  72  -  16, 
71-14,  72-15,  70-15,   69-14,   71-15,   70-15,  69-14, 
71_16,   71-15,   71-14,    70-15,    68-14,    73-16,    73-15, 
70-14,  70-14,  71-15,  73-16,  74-18,  71-13,  73-16. 
Find  the  cost  at  11^  per  pound. 

12.  The  gross  weight  in  pounds,  and  the  tare  in  pounds,  of 
25  casks  of  hams  are  as  follows  :     400  -  78,  420  -  68,  420  -  71, 
403-71,   409-71,   418-68,    412-72,   407-67,    423-69, 
419-67,426-68,    403-70,    399-69,    400-69,    425-71, 
413-72,    399-67,    412-72,    418-68,    409-71,    408-70, 
412-68,   402-71,    421-71,    403-71.      Find   the   cost   at 

per   pound. 


MULTIPLICATION 


55 


SHORT  METHODS   IN   MULTIPLICATION 

81.  There     are      many     short 
methods  in  multiplication,  but  of 
these  only  a  few  are  practical,  either 
because    they   generally    apply  to 
problems   that    in   themselves  are 
not  practical  or  because  they  have 
been  supplanted  by  the  elaborate 
use  of  tables  and  mechanical  de- 
vices.   Many  practical  tables  are  in 
use  for  figuring  pay  rolls,  interest, 
discount,  and  the  like.    (See  pages 
224   and   315.)     Multiplying   ma- 
chines are  also  used  in  many  offices. 

In  the  margin  is  a  picture  of  a  multiplying  machine. 

82.  The  short  methods  given  herewith  have  a  wide  applica- 
tion.    They  are  not  dependent  upon  formal  rules,  and  are  sug- 
gestive of  many  other  ways  in  which  the  student  may  exercise 
his  own  ingenuity  to  shorten  his  work  in  multiplication. 

MULTIPLICATION  BY  POWERS  AND  MULTIPLES  OF  TEN 

ORAL    EXERCISE 

1.  40  is  how  many  times  4?    60  is  how  many  times  6?    100 
is  how  many  times  10?     150  is  how  many  times  15? 

2.  Give  a  short  method  for  multiplying  an  integer  by  10. 

3.  400  is  how  many  times  4?      600  is  how  many  times  6? 
1000  is  how  many  times  10?     1500  is  how  many  times  15? 

4.  Give  a  short  method  for  multiplying  an  integer  by  100; 
by  1000 ;  by  10000. 

5.  How   does   the   product   of    40  x  66    compare    with   the 
product  of  4  x  66  x  10  ?  the  product  of  400  x  59  with  the  prod- 
uct of  4  x  59  xlOO? 

6.  Give  a  short  method  for  multiplying  an  integer  by  any 
number  of  10's,  100's,  or  1000's. 


56  PRACTICAL   BUSINESS   ARITHMETIC 

7.    Multiply  270  by  300. 

SOLUTION.     In  the  accompanying  illustration  ^™ 

it  will  be  seen   that  270  x  300  =  27  x  3  x  1000  300    =     3  X  100 


or  81,000.  81000  =  81  X  1000 

8.  Formulate  a  rule  for  finding  the  product  when  there  are 
zeros  on  the  right  of  both  factors. 

9.  |7  is  how  many  times  10.70?    $90  is  how  many  times 
$0.90?   $500  is  how  many  times  $0.50? 

10.  State   a   short  method  for   multiplying   United   States 
money  by  10 ;  by  100 ;  by  1000. 

11.  Read  aloud  the  following,  supplying  the  missing  words : 
(a)    Annexing  a  cipher  to  an  integer  multiplies  the  integer 

by ;  annexing  two  ciphers  to  an  integer the  integer 

by . 

(6)  Removing  the  decimal  point  in  United  States  money 
one  place  to  the  right  -  -  the  number  by  10;  removing  the 
decimal  point  two  places  to  the  right  -  -  the  number  by . 

12.  Multiply  $14.70  by  10;  by  100;  by  1000. 

83.    In  the  above  exercise  it  is  clear  that 

Annexing  a  cipher  to  an  integer  multiplies  the  integer  by  10; 
and 

Removing   the   decimal  point  one  place  to  the  right  multiplies . 
the  number  by  10. 

ORAL  EXERCISE 

1.  Read  aloud  the  following  numbers  multiplied  by  10 ;  by 
100;  by  1000:     17;  285;  3712;  $413.45 ;  $1926.75;  4165.95. 

2.  Read  each  of  the  following  numbers  multiplied  by  20;  by 
400;  by  600;  by  5000:      16 ;  19 ;  37 ;  49^;  64^;  $122;  $2.60. 

3.  By  inspection  find  the  cost  of : 

a.  750  Ib.  coffee  at  30^.  g.  650  yd.  silk  at  $1.20. 

b.  500  Ib.  cocoa  at  40^.  h.  140  bu.  beans  at  $3.50. 

c.  650  Ib.  chocolate  at  30^.  i.  500  bu.  beans  at  $2.50. 

d.  300  bbl.  lump  salt  at  $3.  /.  240  gro.  jet  buttons  at  $3. 

e.  200  bbl.  oatmeal  at  $4.50.  k.  500  doz.  half  hose  at  $5.50. 
/.  170  bx.  wool  soap  at  $3.  1.  800  yd.  taffeta  silk  at  $1.20. 


MULTIPLICATION  57 

84.  When  the  multiplier  is  a  number  a  little  less  than  10, 
100,  or  1000,  the  multiplication  may  be  shortened  as  shown 
in  the  following  examples. 

85.  Examples.     1.    Multiply  123  by  99. 

1 9300 

SOLUTION.    99  is  100  diminished  by  1;  hence,  multiply  123 

by  100  and  then  by  1  and  subtract  the  results.    The  product  is  123 

12,177.     Check  by  retracing  the  steps  in  the  process.  12177 

2.    Multiply  145  by  96. 

SOLUTION.     96  is  100    diminished  by  4  ;  hence,  multiply  145  1450C 

by  100  and  then  by  4  and  subtract  the  results.    The  product  is  580 

13,920.     Check  by  retracing  the  steps  in  the  process.  13920 

WRITTEN   EXERCISE 

1.    Find  the  total  cost  of  : 

5260  bu.  rye  at  99^.  834  bu.  millet  at  95^. 

1521  bu.  rye  at  92^.  246  bu.  wheat  at  92^. 

1640  bu.  wheat  at  98^.  998  bu.  millet  at  $51.04.  . 

2994  bu.  millet  at  97^.  998  bbl.  apples  at  $1.05. 

1112  bu.  wheat  at  97^.  893  bkt.  peaches  at  $  1.05. 

2160  bu.  millet  at  90^.  993  bu.  clover  seed  at  §3.35. 

MULTIPLICATION  BY  11  AND  MULTIPLES  OF  11 

86.  Example.     Multiply  237  by  11. 

SOLUTION.  To  multiply  by  11  is  to  multiply  by  10  -f  1.  Hence,  annex  a 
cipher  to  237  and  add  237  ;  or,  better  still,  add  the  digits  as  follows  :  7  ;  3  +  7  = 
10  ;  3  +  2+1  (carried)  =  6  ;  bring  down  2  ;  therefore,  the  result  is  2607. 

ORAL   EXERCISE 

1.  Multiply  each  of  the  following  by  11: 

14;  26;  45;  19;  16;  34;  36;  49;  64;  125;  112;  115; 
128;  192;  175;  116;  142;  $4.95;  19.62;  i>4.41;  $6.82; 
$5.21;  $3.65;  $4.31;  $21.12;  $14.21;  $18.32;  $3.26. 

2.  Find  the  cost  of  11  yd.  at  27^;  at  91^;  at  86^;  at 
95^;  at  $1.49;  at  $1.23;  at  $2.17;  at  $2.31;  at  $2.40;  at 
$2.50;  at  $2.75;  at  $4.35;  at  $3.15;  at  $3.10;  at  $8.13. 


58  PRACTICAL   BUSINESS   ARITHMETIC 

87.    Examples.     1.    Multiply  46  by  22. 

SOLUTION.  22  is  11  times  2.  Multiply  46  by  11  and  by  2,  as  fol- 
lows  :  2  x  6  =  12  ;  write  2  and  carry  1.  4  +  6  =  10  ;2x  10+1  (car- 
ried) =  21  ;  write  1  and  carry  2.  2x4  +  2  (carried)  =  10  ;  write  10. 
'The  result  is  1012.  1012 

2.    Find  the  cost  of  122  bu.  of  potatoes  at  66^  per  bu. 

SOLUTION.     6x2  =  12;    write  2  and  carry    1.     2  +  2  =  4;6x4  j22 

+ 1  (carried)  =  25  ;  write  5  and  carry  2.  1  +  2=3;  6x3  +  2 
(carried)  =  20  ;  write  Oand  carry  2.  6x1+2  (carried)  =  8.  Write 
8.  The  result  is  $80. 52.  80.52 

WRITTEN   EXERCISE 
In  the  following  problems  make  all  the  extensions  mentally. 

1.  Find  the  total  cost  of  : 

11  Ib.  coffee  at  42^.  115  bu.  rye  at  99  £ 

14  doz.  eggs  at  11  £  215  bu.  peas  at 

64  Ib.  cheese  at  11  £  344  bu.  oats  at 

33  bu.  carrots  at  56^.  300  bu.  grain  at 

11  bu.  potatoes  at  65^.  115  bu.  barley  at  88^. 

88  bu.  wheat  at  11.13.  400  bbl.  apples  at  11.65. 

2.  Find  the  total  cost  of  : 

77  bu.  peaches  at  11.85.  820  bu.  rye  at  88^. 

151  bu.  corn  at  66^.  327  bu.  oats  at 

265  bu.  onions  at  22^.  314  bu.  peas  at 

135  bu.  apples  at  33^.  110  bu.  pears  at  11.66. 

241  bu.  turnips  at  44^.  880  bu.  barley  at  11.17. 

112  bu.  tomatoes  at  55^.  100  bu.  quinces  at  $1.60. 

A  careful  computer  checks  his  work  at  every  step.  The  student  who 
forms  the  habit  of  doing  this  in  all  his  computations  will  soon  find  himself 
in  no  need  of  printed  answers  to  problems  involving  only  numerical  calcula- 
tion. 

Checks  for  multiplication  have  already  been  mentioned.  To  guard 
against  large  errors,  it  is  also  important  to  form  a  rough  estimate  of  an 
answer  before  beginning  the  solution.  Thus,  in  finding  the  cost  of  211  yd. 
of  lining  at  32^,  at  once  see  that  the  result  will  be  a  little  more  than  163.00 
(210  times  30^);  this  will  do  away  with  such  absurd  results  as  $6752, 
$075.20,  or  $6.75. 


MULTIPLICATION 
3.    Copy  and  find  the  amount  of  the  following  bill: 

Boston,  Mass.,         July   21,  19 

Mrs.  GEORGE  W.  MUNSON 

168  Huntington  Ave.,  City 

Bought  of  S.  S.  PIERCE  COMPANY 

Terms   Cash 


59 


15 
25 
31 
55 
212 
77 

cs.  Horse-radish       $0.66 
Ib.  Huyler's  Cocoa       .44 
gal.  N.  0.  Molasses      .33 
Ib.  Japan  Tea           .38 
u  Raisins               .11 
pkg.  Yeast  Cakes         .44 

MULTIPLICATION  OF  NUMBERS  FROM  11  TO  19  INCLUSIVE 
88.    Example.     Multiply  18  by  17. 


IT 


SOLUTION.  7  x  8  =  56  ;  write  6  and  carry  5.  7  +  8  (that  is  7x1 
+  1  x  8)  +  5  (carried)  =  20  ;  write  0  and  carry  2.  1  x  1  -f  2  (carried) 
=  3  ;  write  3. 

The  foregoing  method  may  be  summarized  as  follows  : 
Multiply  the  units  of  the  multiplicand  by  the  units  of  the  multiplier  and  write 
the  result  as  the  first  figure  of  the  product.    Add  the  units  in  tie  multiplicand  and 
multiplier  and  write  the  result  as  the  second  figure  of  the  product.     Finally  bring 
down  the  tens  of  the  multiplicand.     Carry  as  usual. 

89.  In  a  similar  manner  multiply  together  all  numbers  of 
two  figures  each  whose  tens  are  alike. 

90.  Example.     1.    Multiply  92  by  97. 


SOLUTION.      7  x  2  =  14  ;  write  4  and  carry  1.       2+7=9; 9x9 


92 


+  1   (carried)  =  82  ;  write  2  and  carry  8.     9x9  +  8  (carried)  =  89.  97 

The  result  is  8942.  8924 

91.    The  above  method  may  be  so  modified  as  to  cover  all 
numbers  of  two  figures  each  whose  units  are  alike. 


60 


PRACTICAL   BUSINESS   ARITHMETIC 


92.    Example.     Multiply  92  by  52. 

SOLUTION.    2x2  =  4;    write  4.     9  +  5  =  14;  2  x  14  =  28  ;    write   8 
and  carry  2.     5  x  9  +  2  (carried)  =  47  ;  write  47.    The  result  is  4784. 

ORAL  EXERCISE 


92 


4784 


State  the  product  of: 

1.  16  x  15.       5.    14  x  16.  9.    19  x  18.  13.  27  x  23. 

2.  17  x  18.       6.    18  x  13.  10.    24  x  25.  14.  31  x  38. 

3.  19  x  13.       7.    18  x  14.  11.    23  x  21.  is.  37  x  32. 

4.  15  x  19.        8.    15  x  14.  12.    24  x  26.  16.  34  x  32. 

WRITTEN  EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally. 


1.  Find  the  total  cost  of  : 
42  Ib.  cocoa  at  48*. 

45  Ib.  cocoa  at  43*. 
54  Ib.  coffee  at  24*. 
15  Ib.  raisins  at  13*. 
17  Ib.  biscuits  at  12*. 

2.  Find  the  total  cost  of  : 
36  yd.  wash  silk  at  26*. 

54  doz.  whalebones  at  94*. 
97  yd.  Amazon  cloth  at  97*. 

17  gro.  bone  buttons  at  19^. 

18  yd.  gunner's  duck  at  17*. 


27  bx.  salt  at  57*. 
23  Ib.  coffee  at  24  *. 
19  Ib.  candy  at  18*. 
32  Ib.  chocolate  at  22*. 
85  Ib.  Oolong  tea  at  35*. 

87  yd.  flannel  at  27  *. 
19  yd.  cottonade  at  14*. 
17  yd.  York  denim  at  15*. 

16  yd.  cotton  cheviot  at  19^. 

17  yd.  Hamilton  stripe  at  12*. 


MULTIPLICATION  BY  NUMBERS  OF  Two  FIGURES  ENDING  IN  1 

93.  Example.     Multiply  412  by  31. 

SOLUTION.  Write  2  in  the  product.  3~~x~~2+  1  (the  tens'  figure 
of  the  multiplicand)  =  7  ;  write  7  in  the  product.  3x1  +  4  (the 
hundreds'  figure  of  the  multiplicand)  =  7;  write  7  in  the  product. 
3  x  4  =  12  ;  write  12.  The  result  is  12,772. 

94.  In  a  similar  manner  multiply  by  all  such  numbers  as  301, 
101,  and  901. 


MULTIPLICATION  61 

95.    Example.     Multiply  126  by  201. 


126 
201 


SOLUTION.  Write  26  in  the  product.  2x6+1  (the  hundreds' 
figure  of  the  multiplicand)  =  13.  Write  3  and  carry  1.  2  x  12  + 
1  (carried)  =  25.  The  result  is  25,326.  25826 

The  two  processes  just  explained  are  the  best  for  making  mental  exten- 
sions on  a  bill  and  the  like.  For  general  work,  however,  many  persons  pre- 
fer the  following  methods : 

First  problem  Second  problem 

412  —  once  the  number  126  =  once  the  number 

1236    =  30  times  the  number  252      =  200  times  the  number 

12772  =  31  times  the  number  25326  =  201  times  the  number 

WRITTEN  EXERCISE 
Find  the  product  of: 

1.  214x21.      3.   425x61.  5.   465x121.      7.    746x201. 

2.  315  x  31.      4.   386  x  91.  6.    215  x  401.      8.   859  x  301. 

MULTIPLICATION  BY  NUMBERS  FROM  101  TO  109  INCLUSIVE 

96.  Examples.     1.   Find  the  cost  of  64  bu.  of  wheat  at  $ 1.02. 

SOLUTION.     2  x  64  =  128  ;  write  28  and  carry  1.     1  x  64  +1  = 
65  ;  write  65.      The  result  is  §  65.28.  1.02 

Some  persons  may  prefer  to  work  this  problem  as  follows  :  64  65.28 
bu.  at$l  =$64;  64  bu.  at  2^  =  $1.28;  $64 +  $  1.28  =  $65.28. 

2.    Find  the  cost  of  251  bu.  of  barley  at  $1.04. 

SOLUTION.    4  x  51  =  204  ;   write  04  in  the  product  and  carry  2.  251 

4x2  +  2  (carried)  +  1  (the  right-hand  figure  of  the  multiplicand)  - 

=  11  ;  write  1  and  carry  1.     1  x  25  +  1  (carried)  =  26  ;  write  26. 
The  result  is  $261. 04. 

97.  Similarly  multiply  by  such  numbers  as  201,  302,  and  405. 

98.  Example.     Find  the  cost  of  124  bu.  of  beans  at  8  2.05. 

SOLUTION.     5  x  24  =  120.     Write   20   and   carry    1.      5x1  +  1  124 

(carried)  +2x4  (the  right-hand  figure  of  the  multiplicand)  =  14  ;  205 

write  4  and  "carry  1.     2  x  12  +  1  (carried)  =  25  ;  write  25.     The      - 

result  is  $  254.20.  254.20 

Some  persons  may  prefer  the  following  solution  :  124  bu.  at  $2  =  $248; 
124  bu.  at  5?  =  $6.20;  $248  +  $6.20  =  $254.20.  The  student  should  try 
to  exercise  his  own  ingenuity  in  all  this  work. 


62 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 

Find  the  value  of : 

1.  215  T.  coal  at  $  6.05.  8.  302  bu.  peas  at  74  t. 

2.  224  bu.  rye  at  $1.02.  9.  104  bu.  corn  at  89^. 

3.  215  bu.  wheat  at  $1.02.  10.  103  bu.  beets  at  85  £ 

4.  318  bu.  barley  at  $1.05.  11.  205  bu.  turnips  at  54^. 

5.  124  bbl.  apples  at  $2.05.  12.  215  bu.  pears  at  $1.05. 

6.  116  bbl.  onions  at  $  1.08.  13.  411  bu.  plums  at  $1.08 


7.    232  bbl.  potatoes  at  $2.05.     14.    206  bu.  parsnips  at 

MISCELLANEOUS  SHORT  METHODS 

99.  When  one  part  of  the  multiplier  is  contained  in  another 
part  a  whole  number  of  times,  the  multiplication  may  be  short- 
ened as  shown  in  the  following  examples. 

100.   Examples.     1.    Multiply  412  by  357. 

SOLUTION.  35  is  5  times  7.  7  x  412  =  2884,  which 
write  as  the  first  partial  product.  5  x  2884  =  14,420, 
which  write  as  the  second  partial  product. 

CHECK.  Interchange  the  multiplier  and  multipli- 
cand and  remultiply.  4  x  357  =  1428  ;  3  x  1428  =4284. 
Add.  Since  the  results  by  both  multiplications  agree, 
the  work  is  probably  correct. 


412 

357 

2884 
14420 


357 
412 
1428 
4284 


1470.84   147084 


2.  Multiply  214  by  756. 


214 

756 


SOLUTION.  56  is  8  times  7.  7  x  214  =  1498,  which  write  as  the 
first  partial  product.  8  x  1498  =  11,984,  which  write  as  the  second 
partial  product.  The  sum  of  these  partial  products,  161,784,  is  the 
entire  product. 

Check  as  in  problem  1.     (See  also  pages  83  and  84.)  161784 


1498 
11984 


WRITTEN  EXERCISE 
Find  the  product  of: 

1.  319x248.  3.    728x287.  5.    12816x10217. 

2.  927x279.  4.    848x369.  6.    14416x12525. 
101.    In  multiplying  together  any  two  numbers  of  two  figures 

each,  the  work  may  be  shortened  as  in  the  following  example. 


MULTIPLICATION 


63 


102.    Example.    Multiply  35  by  23. 

SOLUTION.  3x5  =  15;  write  5  and  carry  1.  3x3  +  1  (carried)  + 
2  x  5  =  20 ;  write  0  and  carry  2.  2x3  +  2 (carried)  =  8 ;  write  8.  The 
result  is  805. 


WRITTEN  EXERCISE 

Find  the  product  of: 

1.  23  x  25.         3.   56  x  35.        5.    67  x  51. 

2.  72  x  21.         4.    34  x  52.        6.   86  x  42. 

WRITTEN  REVIEW   EXERCISE 


35 

23 

805 


7.  75x24. 

8.  66  x  82. 


1.  Multiply  .45,216  by  14  412  in  two  lines  of  partial  products. 

2.  Multiply  31,216  by  10,217  in  two  lines  of  partial  products. 

3.  I  bought  15  A.  of  land  at  §275  per  acre  and  laid  it  out  in 
100  city  lots.     After  expending  $6750  for  grading  and  taxes, 
1257  for  ornamental  trees,  and  §250  for  advertising,  I  sold  15 
lots  at  §625  each,  35  lots  at  §415  each,  and  exchanged  the  re- 
mainder for  a  farm  of  120  A.,  which  I   immediately   sold   at 
§195  per  acre.     Did  I  gain  or  lose,  and  how  much? 

4.  Copy  and  find  the  amount  of  the  following  bill: 


July  26,    19 

JMr.  P.  C.  GORHAM 

120  Spring  Street,  City 


Bought  of  C  6.  f  erguson  &  Son 

50  days 


37  bu.  Oats           $0.40 
50   a   Corn             .67 
76  u  Wheat           1.02 
75   u  Rye             1.04 
95   u  Beans           4.00. 
16  u  Clover  Seed      5.50 
26  u  Millet           .99 

CHAPTER  YII 

DIVISION 
ORAL  EXERCISE 

1.  What  is  the  product  of  12  times  15?     How  many  times 
is  15  contained  in  180  ?     What  is  ^  of  180  ? 

2.  How  much  is  11  times  §17?     How  many  times  is  $17 
contained  in  §187  ?     What  is  T\  of  $187  ? 

3.  What  is  the  product  of  9  times  12  ft.?     How  many  times 
is  12  ft.  contained  in  216  ft.?     What  is  ^  of  225  ft.? 

4.  When  one  factor  and  the  product  are  given,  how  is  the 
other  factor  found  ? 

103.  The  process  of  finding  either  factor  when  the  product 
and  the  other  factor  are  given  is  called  division. 

104.  The  known  product  is  called  the  dividend;    the  known 
factor,    the   divisor ;    the   unknown    factor,    when    found,  the 
quotient. 

105.  The  part  of  the  dividend  remaining  when  the  division 
is  not  exact  is  called  the  remainder. 

While  definitions  such  as  the  above  should  not  be  memorized,  the  ideas 
which  they  express  should  be  thoroughly  understood. 

106.  Since  6  times  7  ft.  =  42  ft.,   42  ft.  -=-  7  ft.    =    6,  and 
42  ft.  -r-  6  =  7  ft.     It  is  therefore  clear  that 

1.  If  the  dividend  and  divisor  are  concrete  numbers    the  quo- 
tient is  an  abstract  number  ;  and 

2.  If  the  dividend  is  concrete  and  the  divisor  abstract,  the  quo- 
tient is  a  concrete  number  like  the  dividend. 

In  §106  it  will  be  seen  that  there  are  two  kinds  of  division:  42  ft.-f-  7  ft.  = 
6  is  sometimes  called  measuring,  because  42  ft.  is  measured  by  7ft. ;  42  ft.  •*• 
6  =  7  ft.  is  sometimes  called  partition,  because  42  ft.  is  divided  into  6  equal 
parts. 

64 


DIVISION 


65 


ORAL  EXERCISF 


1. 

Divide 

by 

2: 

18, 

32, 

78, 

450, 

642, 

964, 

893. 

2. 

Divide 

by 

3: 

27, 

57, 

72, 

423, 

642, 

963, 

845. 

3. 

Divide 

by 

4: 

64, 

88, 

92, 

488, 

192, 

396, 

728. 

4. 

Divide 

by 

5: 

65, 

85, 

95, 

135, 

275, 

495, 

725. 

5. 

Divide 

by 

6: 

84, 

9G, 

54, 

246, 

546, 

672, 

846, 

636. 

6. 

Divide 

by 

7: 

63, 

84, 

91, 

217, 

497, 

714, 

791, 

921. 

7. 

Divide 

by 

8: 

72, 

56, 

88, 

248, 

640, 

128, 

144, 

152. 

8. 

Divide 

by 

4: 

56, 

96, 

77, 

241, 

168, 

128, 

920, 

848. 

9. 

Divide 

by 

6: 

78, 

96, 

56, 

272, 

848, 

190, 

725, 

966. 

10. 

Divide 

by 

9: 

98, 

72, 

49, 

279, 

819, 

720, 

189, 

918. 

ORAL  EXERCISE 


1.  16  ft.  -*-  2  =  ?   24  ft. 

2.  825-^5  =  ?    829.75 


8  ft.  =  ? 

5  =  ?   8129.78-^-9  =  ?  13.40 


4  = 


3.  126  yd.  -3  yd.  =  ?     8125  -v-  25  =  ?     86.25  -*-  81.  25  =  ? 

4.  If  9  T.  of  coal  cost  849.50,  what  is  the  cost  per  ton? 

SOLUTION.    $49.50  H-  0  -  $5  ;  subtracting  9  times  $5,  the  re-  85.50 

suit  is  $4.50  undivided;    $4.50  -=-  9  =  $0.50.      Therefore  the          ON~  I0  -A 
quotient  is  $5.50.  i9'D° 

5.  At  -$1.75  a  yard,  how  many  yards  can  be  bought  for  835? 
SOLUTION.     The   divisor  contains   cents    and    it   is  therefore  20 

better  to  first  change  both  dividend  and  divisor  to  cents.    It  is      l7V\Q~£77o 

found  that  $35  would  buy  20  times  as  many  yards  as  $1.75  ,  or 

20yd. 

6.  If  5  T.  of  coal  cost  831.25,  what  is  the  cost  per  ton? 

7.  At  8  2.50  per  yard  how  many  yards  can  be  bought  for  8  550  ? 

ORAL   EXERCISE 

1.  How  many  weeks  in  98  da.  ? 

2.  What  is  fa  of  2250  bbl.  of  apples?  Ty  1?  ^? 

3.  The  quotient  is  8  and  the  dividend  128.      What  is  the 
divisor? 

4.  How  many  times  can  18  be  subtracted  from  75,  and  what 
will  remain? 


6G  PRACTICAL   BUSINESS    ARITHMETIC 

5.  At  15^  per  pound,  how  many  pounds   of  beef  can  be 
bought  for  $6.30? 

6.  The  quotient  is  5,  the  divisor  23,  and  the  remainder  2. 
What  is  the  dividend  ? 

7.  If  5  men  earn  $17.50  a  day,  how  much  can  8  men  earn 
in  2  da.  at  the  same  rate? 

8.  What  is  the  nearest  number  to  150  that  can  be  divided 
by  9  without  a  remainder? 

9.  If  there  are  960  sheets  in  40  qr.   of  paper,  how  many 
sheets  in  5  qr.  ?  in  11  qr.  ? 

10.  If  6   bbl.   of   apples    are  worth  $9,    what   are    24   bbl. 
worth  at  the  same  rate?   36  bbl.? 

11.  If  17  bbl.  of  flour  cost  $85,  what  will  25  bbl.  cost  at  the 
same  rate?  32  bbl.  ?  48  bbl.  ?  34  bbl.  ? 

12.  If  8  be  added  to  a  certain  number,  the  sum  will  be  24 
times  the  number.     What  is  the  number? 

13.  If    20  yd.   of   cloth  cost  $60,  for  how  much   per    yard 
must  it  be  sold  to  gain  $25?    to  gain  $15? 

14.  A  grocer  sold  250  oranges  at  5^  each  and  gained  $5. 
How  much  did  he  pay  a  dozen  for  the  oranges? 

15.  A  grocer  pays  $3  for  20  doz.  of  eggs.     At  what  price  per 
dozen  must  he  sell  them  in  order  to  gain  $1.50? 

16.  At  $2.50   per  yard,  how  many  yards   of  cloth  can   be 
bought  for  $75?  for  $150?  for  $2500?  for  $750? 

17.  How  many  days'  labor  at  $3.50  per  day  will  pay  for  2  T. 
of  coal  at  $7  a  ton  and  5  Ib.  of  tea  at  70^ per  pound? 

18.  A  clothier  pays  $96   for  a  dozen  overcoats.      At  how 
much  apiece  must  lie  retail  them  to  gain  $48  on  the  lot? 

19.  A  man  exchanged  1140  bu.  of  wheat  at  $1  per  bushel 
for  flour  at  $6  per  barrel.      How  many  barrels  did  he  receive? 

20.  It  was  found  that  after  15  had  been  subtracted  5  times 
from  a  certain  number  the  remainder  was  4.     What  was  the 
number? 

21.  A  man  contracts  a  debt  of  $175  which  he  promises  to 
pay  in  weekly  installments  of  $3.50  each.     After  paying  $35, 
how  many  more  payments  has  he  to  make? 


DIVISION  67 

107.    Examples.     1.  Divide  4285  by  126: 

COMPLETE  OPERATION  REQUIRED  WORK 


126)4285  126)4285 

378            =3  times  126  378 

505  undivided  505 

504          =4  times  126  504 

1  undivided  1 

CHECK.     34  x  126  +  1  =  4285 

The  remainder  cannot  always  be  written  as  a  part  of  the  quotient.  Thus 
in  the  problem,  "  At  $7  per  head  how  many  sheep  can  be  bought  for  $37," 
we  cannot  say,  "  5f  sheep,"  but  "  5  sheep  and  $2  remaining." 

2.  A  farmer  received  $283.25  in  payment  for  275  bu.  of  wheat. 
How  much  was  received  per  bushel  for  the  wheat? 

11.03 

SOLUTION.  $283.75-^275  =  $!  and  $8.25  undivided.  275)$ 283.25 
$8.25  •*•  275  =  $0.03.  $1.03  per  bushel  was  therefore  re-  975 

ceived  for  the  wheat.  — 

CHECK.     275  times  $1.03  =  $283.25.  °  *5 

825 

108.  Work  in  division  may  be   abridged   by   omitting   the 
partial  products  and  writing  only  the  partial  dividends. 

109.  Example.     Divide  $614.80  by  232. 


SOLUTION.     2   times  2  plus  0  =  4;    2  times  3   plus  5  = 


11.     2  times  2  +  1  =  5,  and  5  plus  1  =  6.     Bring  down  8.  232)$  614.80 

6  times  2  plus  6  =  18;  6  times  3  plus  1  =  19,  and  19  +  1  =  '  150  8 

20;   6  times  2   plus   2  =  14,    and   14   plus   1  =  15.      Bring  11  60 

down  0  and  proceed  as  before.  0  00 

WRITTEN   EXERCISE 

1.  Find   the   value   of  8800  Ib.  of  oats  at  45  ^   per    bushel 
of  32  Ib. 

2.  How  many  automobiles,  at  1650  each,  can  be  purchased 
for  14,225,000  ? 

3.  By  what  number  must  8656  be  multiplied  to  make  the 
product  8,223,200  ? 


68 


PRACTICAL   BUSINESS   ARITHMETIC 


4.  If  120  bbl.  of  flour  cost  $660,  what  will  829  bbl.  cost  at 
the  same  rate  ? 

5.  The  product  of  two  numbers  is  1,928,205.    If  one  of  them 
is  621,  what  is  the  other? 

6.  If  380  T.  of  coal  can  be  bought  for  83040,  how  many 
tons  can  be  bought  for  $  3600? 

7.  How  many  cords  of  128  cu.  ft.  in  a  pile  of  wood  con- 
taining 235,820  cu.  ft.  ?     What  is  it  worth  at  $4.50  per  cord  ? 

8.  A  speculator  sold  a  quantity  of  apples  that  cost  $2500 
for  $4750.       If   his    gain   per   barrel  was  $1.12|,  how  many 
barrels  did  he  buy  ? 

9.  A  man  received  a  legacy  of  $11,375  which  he  invested 
in  railroad  stock.     He    paid  a  broker   $  125  to  buy  stock   at 
$112.50  per  share.     How  many  shares  were  bought? 

10.  A  dealer  bought  250  T.  of  coal  by  the  long  ton  of  2240 
Ib.  at  $4.50  per  ton.     He  retailed  the  same  at  $6.75  per  short 
ton  of  2000  Ib.     What  was  the  total  gain  ? 

11.  In   a  recent  year  there   were   produced  in   the  United 
States  550,935,925  bu.  of  wheat  on  44,074,874  A.     What  was 
the  yield  per  A.  ?     What  was  the  yield  worth  at  44.9^  per  bu.  ? 

12.  Copy  and  complete  the  following  table  of  corn  statistics. 
Check  the  work.      (The  total  yield  multiplied  by  the  price  per 
bushel  should  equal  the  total  valuation.) 

PRINCIPAL  CORN-GROWING  STATES  IN  A  RKCENT  YEAR 


STATE 

YIELD  IN  BUSHELS 

FARM  PRICE 
I-ER  BUSHEL 

KAU.M  VALUATION 

Illinois 

334  133  680 

44^ 

147018819 

20 

Iowa 

44? 

133  337  277 

04 

Nebraska 

44  ? 

114814627 

40 

Missouri 

44? 

66  669  962 

92 

Indiana 

143  396  852 

44? 

Texas 

136  702  6!)9 

44? 

Total 

13-15.    Make  and  solve  three  self -checking  problems  in  division. 


DIVISION  69 

SHORT   METHODS    IX  DIVISION 

POWERS  AND  MULTIPLES  OF  10 

ORAL  EXERCISE 

1.  How  many  times  is  10   contained  in  50?  100  in  800? 
1000  in  9000? 

2.  Catting  off  a  cipher  in  30  divides  it  by  what  number? 

3.  Cutting  off  two  ciphers  in  800  divides  it  by  what  number? 

4.  Cutting  off  three  ciphers  in  11,000  divides  it  by  what 
number  ? 

5.  Read  aloud,  supplying  the  missing  words  : 

a.  The  number  of  10's  in  any  number  may  be  found  by 
cutting  off  the  units'  figure  ;  the  number  of  100's  by  cutting 
off  the  -  and  -  figures  ;  the  number  of  -  -  by  cutting 
off  the  hundreds'  and  tens'  and  units'  figures. 

b.  In  4561  there  are  456  tens  and  1  unit,  or  456^  tens;  45 
-  and  61  units,  or  45-j^g-  hundreds;  and  --  thousands  and 


561  units,  or  4^^  thousands. 

6.  How   many  times  is  $0.10   contained  in  $  1  ?  $0.01  in 
$1?  $0.001  in$l? 

7.  What  is'^  of  $1?     T1L  of  $1  ?     loVo  of  #1? 

8.  Read  aloud,  supplying  the  missing  words:  $0.60  is  - 
of  $6  ;  $0.06  is  -  of  $6  ;     $0.006  is  --  of  $6. 

9.  Formulate  a  short  method  for   dividing    United  States 
money  by  10;  by  100;  by  1000. 

10.  By  inspection  find  the  quotient  of  : 

a.  736-s-lO.  e.  $271  -s-  100.         i.  2140  Ib.  -f-  100. 

b.  1531-100.  /.  $519.50-10.     j    3145  Ib.  -s-  100. 

c.  16351-1000.         #.$84.50-100.      k.  3416  ft.  -r-  1000. 

d.  311219-10000.     h.  $2150-1000.     I.  1279  posts  -*-  100. 

11.  Read  aloud,  supplying  the  missing  amounts  : 

a.  6400-1600  =  -    -;   640-10  =  --  . 

b.  27000-9000  =  -  j    2700-900=  --  ;    270  -r-  90  = 
-  ;  27-9=  --  . 

c.  18801  -  90  =  -  -  9  ;  214200  -  700  =  2142  -  -  . 


70  PEACTICAL   BUSINESS   ARITHMETIC 

12.  How  is  the  quotient  affected  by  like  changes  in  both 
the  dividend  and  divisor  ? 

13.  Divide  1323  by  400. 

SOLUTION.     Cut  off  the  two  ciphers  in  the  divisor  and  two 
digits  in  the  right  of  the  dividend,  thus  dividing  both  dividend  4|00")13I23 
and  divisor  by  100.     4  is  contained  in  13  three  times  with  a 
remainder  1  hundred.     Adding  to  this  remainder  the  23  units 
remaining  in  the  dividend  after  dividing  by  100,  the  true  re-  123 

mainder  is  123,  which  write  in  fractional  form. 

14.  Read  aloud,  supplying  the  missing  amounts  :   1611  —  400 
-;     2847-700  =  -    -;    1531-300  =  -    -;    16139-*- 

4000  = . 

15.  Formulate  a  rule  for  dividing  a  number  by  any  multiple 
of  ten. 

16.  State  the  quotient  of  : 

a.  1231-30.  /.  96131-400.  k.  63571 -r- 3000. 

b.  9647-40.  g.  84199-700.  I.  16657 -=- 4000. 

c.  6551^50.  h.  64137 -v- 800.  m.  36119-=- 6000. 

d.  4273-70.  i.  45117 -s- 900.  n.  18177^9000. 

e.  8197^-90.  i.  25121-500.  o.  42113^7000. 


ORAL  REVIEW  EXERCISE 

The  diagram  on  the  opposite  page  is  a  portion  of  the  New  York  Central 
time-table  giving  the  distances  between  many  of  the  stations  from  New 
York  City  to  Suspension  Bridge,  and  the  time  taken  by  two  different  trains 
to  travel  this  route. 

1.  How   many  miles  between  New   York  City  and  Pough- 
keepsie?  between  Poughkeepsie  and  Utica  ?  between  Utica  and 
Syracuse?  between  Syracuse  and  Rochester?  between  Rochester 
and  Buffido?  between  Buffalo  and  Niagara  Falls? 

2.  What  is  the  distance  between  New  York  City  and  Syra- 
cuse?   between    Poughkeepsie    and    Niagara   Falls?   between 
Rochester   and    Suspension    Bridge? 

3.  How  many  miles  between  Ludlow  and  each  station  below 
it?  between  Poughkeepsie  and  each  station  below  it?  between 
Tarry  town  and  each  station  below  it? 


DIVISION 


71 


4.  How  many   miles  between   Montrose   and   each 
below   it?    between   Oscawana  and 

each  station  below  it? 

5.  At  2^  per  mile,  what  is  the 
fare    from    New    York   to   Niagara 
Falls?  from  Poughkeepsie  to  Syra- 
cuse ?  from  Buffalo  to  Utica  ?   from 
Troy  to  Yonkers? 

6.  At  2^  per  mile,  what  is  the 
fare   from   Rochester  to   Syracuse? 
from     Rensselaer     to      Suspension 
Bridge?    from   Albany   to  Niagara 
Falls?    from  Syracuse  to  Buffalo? 
to  Albany? 

7.  How  long  does  it  take  train 
No.   93  to  travel  the  first  30  mi. 
toward  Poughkeepsie?  the  first  74 
mi.  toward  Albany? 

8.  How  long   is   train   No.    93 
in  making  the   run   from   Fishkill 
Landing  to  Camelot?     This  is  ap- 
proximately   how    many    miles    an 
hour? 

9.  How  long  does  it  take  train 
No.  73  to  make  the  run  from  Utica 
to  Syracuse?    How  long  does  it  take 
train  No.  73  to  make  the  run  from 
Fishkill  Landing  to  Chelsea?    This 
is  approximately  how  many  miles 
an  hour? 

10.  Add  each  number  in  the  col- 
umn marked  "  Miles "  to  the  one 
immediately  below  it. 


station 


Thus,  9, 12, 16, 24, 34, 45, 58,  etc.  In  add- 
ing 89  and  95  think  of  179  and  5,  or  184 ;  in 
adding  143  and  149  think  first  of  243  afid  49  and  then  of  283  and  9,  or  292. 


I 

NORTH 
AND 
WEST  BOUND 

Midnight 
Express 

** 

II 

1 

73 

93 

0 
4 
5 
7 
8 
10 
11 
13 
14 
15 
16 
18 
20 
21 
22 
23 
26 
30 
31 
35 
37 
38 
39 
42 
47 
50 
53 
56 
58 
59 
63 
65 
69 
74 
74 
80 
84 
89 
95 
99 
105 
109 
111 
115 
119 
[22 
125 
131 
135 
142 
143 
149 

New  York 
Grand  Cent.  Sta  Lv. 
125th  St.  Sta  " 
138th  St.  Sta.  " 
High  Bridge  " 
Morris  Heights  " 
Kings  Bridge  " 
Spuyten  Duyvil  " 
Riverdale  " 
Mt.  St.  Vinceut  " 
Ludlow  " 
Yonkers  .*....  .              " 

121J10 
12*23 

^ 

I 
I 

12.46 

T09 
'l.25 

GfOl 
6*,13 
6.15 
6.21 
6.25 
6.29 
6.33 

6.43 
6.46 
6.52 
6.59 
7.01 
7.05 
7.12 
7.19 
7.25 
7.31 
7.34 
7.37 
7.41 
7.49 
7.59 
8.06 
8.12 
8.16 
8.21 
8.27 
8.34 
8.40 
8.46 
8*55 

Glenwood                     " 

Hastings-on-Hudson  " 
Dobbs'  Ferry  " 
Ardsley-  on  -Hudson  " 
Irvington  " 
Tarrytown  " 

Scarborough  " 
Ossining  " 
Croton-on-Hudson  ..  " 
Oscawana  " 
Crugers                         " 

Montrose.  ..             ..  " 
Peekskill                      " 

1A7 

X 

X 

224 
2.31 

Highlands  " 
Garrison  " 
Cold  Spring                  " 

Storm  King  " 
Dutchess  June            " 
Fishkill  Landing  " 
Chelsea  " 
New  Hamburg            " 

Camelot  " 

"2.53 
3.05 

Poughkeepsie  Ar. 
Poughkeepsie               Lv. 

Hyde  Park  " 
Staatsburgh  " 
Rhinecliff  (Rh'b'k)..  " 
Barrytown                   " 
Tivoli 

Germantown  " 

Linlithgo  " 
Greendale                    " 

Hudson  :  " 

4.47 

Stockport  " 
Newton  Hook             " 

Stuyvesant  " 
Schodack  Landing..  " 
Castleton  " 

Rensselaer                   " 

"5.50" 

C*,50 

....... 

Albany  Ar. 
Troy  " 

238 
291 
371 
440 
463 
464 

Utica  Ar. 

8^40 
9.55 
11.38 
1MP15 

Rochester                      " 

Buffalo  " 

Niagara  Falls  Ar. 
Suspension  Bridge  

2513 

2£20 

72  PRACTICAL   BUSINESS   ARITHMETIC 

11.  Multiply  each  number  in  the    column   marked  "Miles" 
by  5 ;   by  8;  by  3;  by  7;   by  6  ;  by  4  ;  by  9. 

The  numbers  in  the  portion  of  the  time-table  illustrated  may  be  used  for 
such  other  exercises  as  may  seem  necessary  at  this  point.  Students  should 
be  impressed  with  the  importance  of  being  able  to  add,  subtract,  multiply, 
and  divide  numbers  in  any  relative  position. 

12.  Five  parts  of  120  are  15, 18,  32,  10,  and  20.     Find  the 
sixth  part,  and  multiply  it  by  15. 

13.  From  a  flock  of  170  sheep  I  sold  at  different  times  12, 
18,  32,  and  9.     How  many  sheep  remained? 

14.  Multiply  each  of  the  following  numbers  by  11 :  21,  32, 
43,  54,  65,  76,  87,  98,  61,  28,  37,  14,  21,  62. 

15.  At  22^  per  yard,  what  will  18  yd.   cost?    21  yd.?    36 
yd.  ?  56  yd.  ?  29  yd.  ?     73  yd.  ?  94  yd.  ?  72  yd.  ? 

16.  Multiply  each  number  in  problem  15  by  33  ;  by  44. 

17.  Multiply  each    number  in   problem  15  by  10;   by  100; 
by  30  ;  by  300  ;  by  500. 

18.  What  will   102    bu.   of  wheat  cost  at  68^  per  bushel? 
at  82^  per  bushel?  at  91^  per  bushel?  at  99^  per  bushel? 

19.  Find  the     cost      of    32    bu.    of    apples     at    45^    per 
bushel;  at    38^  per  bushel;  at   42^  per    bushel;   at    28^   per 
bushel;  at  15^  per  bushel  ;  at  21^  per  bushel. 

20.  I  have  on   hand   at    the    opening    of    business  Monday 
morning  cash  amounting  to  1800.       I  pay  out  $80,  $40,  arid 
$30  and  have  on   hand   at   the  close  of  the  day  $860.     How 
much  cash  did  I  receive  during  the  day? 

Postal  information.  All  mailable  matter  for  transmission  by  the  United 
States  mails  within  the  United  States  or  to  Cuba,  Mexico,  Hawaii,  Porto 
Rico,  Canada,  and  the  Philippine  Islands  is  divided  into  four  classes :  first- 
class  matter,  second-class  matter,  third-class  matter,  and  fourth-class  matter. 

First-class  matter  includes  letters,  postal  cards,  and  anything  sealed  or 
otherwise  closed  against  inspection.  The  rate  for  first-class  matter  is  2  ^ 
per  ounce  or  fraction  thereof.  The  cost  of  an  ordinary  postal  card  is  1^; 
of  a  reply  postal  card,  2  ^. 

Second-class  matter  includes  newspapers  and  periodicals  entirely  in  print. 
When  sent  by  publishers  or  news  agents,  the  rate  is  1  ^  per  pound  or  fraction 
thereof ;  when  sent  by  others,  1  ^  for  each  4  oz.  or  fraction  thereof. 


DIVISION  73 

Third-class  matter  includes  books,  circulars,  pamphlets,  proof  sheets  and 
manuscript  copy  accompanying  the  same,  and  engravings.  The  rate  is  1  ^ 
for  each  2  oz.  or  fraction  thereof. 

The  limit  of  weight  in  third-class  matter  is  4  lb.,  except  single  books  in 
separate  packages,  on  which  the  weight  is  not  limited. 

Fourth-class  matter  includes  all  mailable  matter  not  specified  in  the  pre- 
ceding classes,  such  as  merchandise  and  samples  of  every  description  and 
kind  and  specie.  The  rate  is  1  ^  for  each  ounce  or  fraction  thereof. 

All  kinds  of  postal  matter  may  be  registered  at  the  rate  of  8^  for  each 
package  in  addition  to  the  regular  rates  of  postage. 

The  rates  on  special  delivery  letters  are  10  f-  per  letter  in  addition  to 
the  regular  postage.  Any  matter  on  which  a  special  delivery  stamp  is 
affixed  is  entitled  to  special  delivery. 

Foreign  rates  of  postage  are  as  follows:  letters  5^  per  half  ounce  ;  postal 
cards,  2  ?;  newspapers  and  other  printed  matter,  1  ?  per  every  2  ounces. 

21.  What  is  the  postage  on  a  letter  weighing  |  oz.?  4|oz.? 
1J  oz.?  3  £  oz.?  2|  oz.?  4J  oz.? 

22.  Find  the  total  cost  of  mailing  the  following  to  points 
in  Canada:   a  book,  weighing  32 1  oz.,  which  you  have  regis- 
tered; a  package  of  jewelry,  weighing  19  oz.,  which  you  have 
registered. 

23.  What  will  be   the  total  cost  of  mailing    the  following 
articles  at  your  post  office  to  points  within  the  United  States: 
an  ordinary  letter,  weighing  2  J  oz.  ;  a  registered  letter,  weigh- 
ing 1 J  oz.  ;    a  book,  weighing  3  lb.   8   oz. ;    and    a  bundle  of 
papers,  weighing  10  oz.? 

24.  Find  the  total  cost  of  mailing  the  following  to  points 
within  the  United  States  :  a  special  delivery  letter,  weighing 
1J  oz. ;  a   registered   letter,  weighing   2|   oz.;    some  printers' 
proofs,  weighing  18  oz.;   some  separate  manuscript  for  printer, 
weighing  12  oz. ;  a  pamphlet  weighing  6  oz. 

25.  Find  the  mailing  price  of  each  of  the  following  articles  : 

ARTICLE  LIST  PRICE     WEIGHT  WHEN  PACKED 

a.  A  pair  of  opera  glasses  $12.50  2  lb.  8  oz. 

b.  A  pair  of  ladies'  gloves  $  2.50  6  oz. 

c.  A  copy  of  Star-Land  $1.20  lib.  8  oz. 

d.  A  copy  of  Whittier's  Poems  $  1.60  1  lb.  12  oz. 

e.  A  copy  of  Footprints  of  Travel  8  1.25  1  lb.  8  oz. 


74  PRACTICAL   BUSINESS   ARITHMETIC 

26.  A  publishing  house  advertises  books  at  the  following 
prices.     If  the  wrapping  used  in  preparing  the  books  for  mail- 
ing weighs  4  oz.  in  each  case,  what  is  the  weight  of  the  book  ? 

BOOK  LIST  PRICE  MAILING  PRICE 

a.  Wilderness  Ways  45^ 

b.  Ways  of  Woodfolk  50^ 

c.  Friends  and  Helpers  60^  70  ^ 

d.  Triumphs  of  Science  30^  35  j^ 

e.  Industries  of  To-day  25^  30^ 

27.  A  publisher  sends  20,000  copies  of  his  magazine  by  mail. 
If  each  magazine  and  wrapper  weighs  14|  oz.  and    the  total 
number  is  weighed  at  the  post  office  in  bulk,  what  will  the  pub- 
lisher have  to  pay  for  postage  ? 

28.  A  subscriber  mails  two  issues  of  the  above  magazine  to  a 
friend.     What  will  be  the  cost  for  postage  ? 

29.  25,000  copies  of  a  monthly  magazine  weighing  14^  oz. 
were  sent   by   mail.     What  is  the  cost   to   the   publisher   of 
mailing  ? 

30.  Find  the  total  cost  for  mailing  the  following  :  printers' 
proof  weighing  18J  oz.  ;  manuscript  and  printers'  proof  in  one 
package,  weighing  28J  oz.  ;  a  book,  weighing  22  oz". ;  a  special 
delivery  letter,  weighing  |  oz. ;  two  ladies'  pocketbooks,  weigh- 
ing 14  oz. 

WRITTEN  REVIEW  EXERCISE 

l.  Find  the  total  cost  of  the  articles  in  problem  3  of  the  oral 
exercise,  page  56.  Find  the  total  of  the  products  in  the  oral 
exercise,  page  60. 

2.  A  mechanic  earns  $125  per  month  and  his  monthly  ex- 
penses average  $72.     If  he  saves  the  remainder,  how  long  will 
it  take  him  to  pay  for  a  house  costing  $4352  ? 

3.  I  spent  $24,800  for  apples  at  $2.50  per  barrel.     The  loss 
from  decay  was  equal  to  74  bbl.     What  was  my  gain,  if  the 
remainder  of  the   apples   sold   for    $3.75  per  barrel,  and  my 
expenses  for  storage  were  $675.80? 


DIVISION 


4.  Without  copying  find  (a)  the  total  number  of  railway 
employees  in  the  United  States  in  1903  and  (6)  the  total  num- 
ber per  hundred  miles  of  line  in  the  same  year. 

RAILWAY  EMPLOYEES   iv  THE  UNITED  STATES 


1904 

1903 

CLASS 

TOTAL 
NUMBER 

NUMBER  PEK 
100  MILES 

AVERAGE 
DAILY  WAGES 

TOTAL 
NUMBER 

NUMBER  PER 
100  MILES 

AVERAGE 
DAILY  WAGES 

General  officers 

5,165 

2 

$11.61 

4,842 

2 

$11.27 

Other  officers 

5.375 

3 

6.07 

5,201 

3 

5.76 

General  office  clerks 

46,037 

22 

2.22 

42,218 

21 

2.21 

Station  agents 

34,918- 

16 

1.93 

34,892 

17 

1.87 

Other  statioumen 

120,002 

57 

1.C9 

120,724 

59 

1.64 

Engineers 

52,451 

25 

4.10 

52,993 

26 

4.01 

Firemen 

55,004 

26 

2.35 

56,041 

27 

2.28 

Conductors 

39,645 

19    • 

3.50 

39,741 

19 

3.38 

Other  trainmen 

106,734 

50 

2.27 

104,885 

51 

2.17 

Machinists 

46,272 

22 

2.61 

44,819 

22 

2.50 

Carpenters 

53,646 

25 

2.26 

56,407 

27 

2.19 

Other  shopmen 

159,472 

75 

1.91 

154,635 

75 

1.86 

Section  foremen 

37,609 

18 

1.78 

37,101 

18 

1.78 

Other  trackmen 

289,044 

136 

1.33 

300,714 

147 

1.31 

All  other  employees 

244,747 

115 

1.98 

257,324 

125 

1.93 

5.  Without  copying  find  (a)    the  total  number  of  railway 
employees  in  the  United  States  in  1904  and  (6)  the  total  num- 
ber per  one  hundred  miles  of  line  in  the  same  year. 

6.  Find  the  total  salaries  paid  to  railway  employees  in  1903  ; 
in  1904. 

7.  Find  the  average  daily  wages  paid  to  railway  employees 
in  1903  ;  in  1904. 

8.  During   a  certain   week  a  contractor  employed  help   as 
follows:   34  hands,  8  hr.  per  day,  for  5  da.,  at  15^  per  hour  ; 
16  hands,  9  hr.  per  day,  for  6  da.,  at  25^  per  hour  ;   29  hands, 
10  hr.  per  day,  for  6  da.,  at  18^  per  hour.     Find  the  amount 
due  the  employees. 

9.  In  a  recent  year  there  were  produced  on  27,842,000  A.  in 
the  United  States  863,102,000  bu.  oats,  valued  on  the  farm  at 
31.3^  per  bushel.     What  was  the  average  yield  per  acre?  what 
was  the  value  of  the  year's  crop  ? 


76 


PRACTICAL   BUSINESS   ARITHMETIC 


10.  Complete  the  following  schedule  by  finding  the  vertical 
and  horizontal  totals.  Check  the  work  by  comparing  the  sum 
of  the  vertical  totals  with  the  sum  of  the  horizontal  totals. 

SALARY  AND   EXPENSE  SCHEDULE 

Fish  and  Game  Commission  of  Massachusetts 


FOR    THE    MONTH    ENDING. 


-,   ?/7. 


COMMISSIONERS 


SALARY    EXPENSE 


SALARY    EXPENSES 


16 


2 


DIVISION 


77 


11.    Without  copying,  find  quickly  the  total  amount  of  the 
following  manufacturer's  time  sheet.      Check  the  work. 

TIME    SHEET   FOR   WEEK   ENDING  JULY    29 


NAME 

M. 

T. 

w. 

T. 

F. 

s. 

TOTAL 
TIME 

KATE 
NEB 

HOUR 

AMOUNT 

Harry  Ball     .... 

9 

8 

10 

10 

10 

9 

0? 

John  Cook      •     .     .     . 

8 

8 

10 

9 

9 

8 

12^ 

James  Easton     .     .     . 

9 

9 

9 

10 

8 

8 

Itf 

Frank  King    .... 

7 

6 

8 

9 

9 

10 

20? 

Paul  Mason   .... 

8 

8 

8 

8 

8 

8 

25? 

12.  From  the  following  data  make  a  statement  of  losses  and 
gains  :   Market  value  of  groceries  on  hand  May  1,  84469.40. 
Bought  groceries  during  the  month:   for  cash,   $1279.60;    on 
credit,  $2150.40.     Sold  groceries  during  the  month:  for  cash, 
$2160.40;  on  credit,  $2640.10.     Gross  expenses  at  the  close 
of  the  month,  $590.50.     Account  against  J.  E.   Brown  &  Co. 
which  cannot  be  collected,  $79.80.     Market  value  of  groceries 
on  hand  at  the  close  of  the  month,  $2842.60.     Required,  the 
net  gain  or  net  loss. 

13.  In  the  following  table  find  (a)  the  total  number  of  tickets 
sold  each  day,  (&)  the  total  number  of  each  class  sold  during 
the  week,  and  (c)  the  aggregate  number  of  tickets  sold  during 
the  week.     Check  the  work. 

TICKETS   OF   ADMISSION   SOLD   AT   A    STATE    FAIR 


CLASS 

PRICE 

MONDAY 

TUESDAY 

WEDNESDAY 

THURSDAY 

FRIDAY 

SATURDAY 

TOTAL 

Children 

$  0.35 

1240 

1242 

4165 

3169 

3146 

1240 

Adults 

.75 

6129 

6129 

12168 

17246 

12174 

9167 

Single  carriages 

.75 

68 

126 

329 

278 

278 

74 

Double  carriages 

1.25 

49 

114 

215 

210 

210 

62 

Total 

14.    In  the  above  table  find  (a)  the  daily  receipts  from  tickets 
and  (5)  the  aggregate  receipts  for  the  week.     Check  the  work. 


78 


PRACTICAL   BUSINESS   ARITHMETIC 


Copy  the  following  time  sheets  and  find  («)  the  total  number 
of  hours  worked  on  each  order,  (£)  the  total  number  of  hours 
worked  each  day,  (<?)  the  amount  earned  on  each  order,  and 
the  total  amount  earned  during  the  week.  Check  the  work. 

15. 
BOSTON    ELEVATED    RAILWAY    COMPANY 


Time  worked  Ky 


During  the  week  ending- 
Rate  per  hour_s-£-Ol 


.^^^7     y/T 


Occupation- 


Sun.  Moo.  Tue 


Wed.  Thur. 


16. 
BOSTON    ELEVATED    RAILWAY    COMPANY 


Time  worked  by 


During  the  week  ending- 
Rate  per  hour 


Occupation. 


>-3  2- 


CHAPTER   VIII 

AVERAGE 
ORAL   EXERCISE 

1.  A  earns  $3,  B  earns  $4,  and  C  earns  $5  per  day.     What 
do  the  three  earn  in  1  da.?     If  $12  were  paid  to  these  men  in 
equal  parts,  how  much  would  each  receive  ? 

2.  What  sum  is  intermediate  between  6,  7,  and  8  ?  between 
6,  8,  and  10  ?  between  6,  12,  and  18  ? 

110.  The  process  of  finding  a  number  that  is  intermediate 
between  two  or  more  other  numbers  is  called  average. 

111.  Example.     What  is  the  average  weight  of  3  bales  of 
cotton  weighing  460,  449,  and  475  lb.,  respectively? 

SOLUTION.  The  aggregate  of  the  3  bales  of  cotton  is  1384  lb. 
1384  lb.  divided  into  three  equal  parts  shows  the  mean  or  average 
weight  to  be  4611  lb. 

To  find  the  average  of  consecutive  numbers,  add  the  highest 
number  to  the  lowest,  and  divide  by  2.  ^ 

WRITTEN  EXERCISE 

- 

1.  A  tapering  board  is   14  in.  wide  on  one  end  and  18  in. 
on  the  other.     What  is  the  average  width  of  the  board? 

2.  A  manufacturing  pay  roll  shows  that  15  hands  are  em* 
ployed  at  $1.25  per  day,  12  hands  at  SI. 75  per  day,  16  hands 
at  $2.25  per  day,  32  hands  at  $2.50  per  day,  and  5  hands  at 
$6.50  per  day.     Find  the  average  daily  wages. 

3.  A  merchant's  sales  for   a  year  were  as  follows :  January, 
$12,156;  February,  $14,175;  March,  $16,152;  April,  $12,175; 
May,  $12,465. 95;  June,  $12,476.05  ;  July,  $15,145.40  ;  August, 
$12,431.46;     September,    $17,245.90;     October,   $18,256.45; 
November,  $19,250.65;    December,  $19,654.20.      What  were 
his  average  sales  per  month? 

79 


80 


PRACTICAL   BUSINESS   ARITHMETIC 


4.  In  a  certain   school  of  300  pupils,  85  are  14  yr.  of  age ; 
50,  15  yr.  of  age ;  25,  16  yr.  of  age ;  75,  17  yr.   of  age ;  50, 
18  yr.  of  age;  15,  19  yr.  of  age.     What  is  the  average  age  of 
the  school? 

5.  The  attendance  for  a  certain  school  for  a  week  was  as  fol- 
lows :  Monday,  727  pupils  ;  Tuesday,  732  pupils  ;   Wednesday, 
756  pupils;   Thursday,  761  pupils;   Friday,  734  pupils.     What 
was  the  average  daily  attendance  for  the  week  ? 

6.  What  should   a  ground  feed    made  from  50  bu.  of  oats 
worth   28^  per    bushel,   30    bu.    of  barley   worth  78^,  and  60 
bu.   of  corn    worth    59^  sell   for   in  order    to    make    10^    per 
bushel  on  each  ingredient  used  to  make  the  mixture? 

7.  Find  the  aggregate  weight  and  the  average  weight  per 
box  of  100  bx.  of  cheese  weighing  65,  64,  62,  60,  61,  65,  62,  64, 

61,  62,  61,  60,  60,  61,  62,  60,  68,  65,  66,  64,  62,  61,  65,  66,  62, 

64,  67,  58,  62,  59,  59,  60,  62,  64,  66,  67,  58,  60,  65,  58,  62,  69, 

62,  65,  68,  69,  61,  65,  62,  61,  65,  68,  59,  62,  64,  58,  62,  65,  71, 
70,  58,  67,  58,  62,  64,  58,  62,  64,  65,  69,  65,  65,  62,  64,  60,  60, 

65,  60,  65,  65,  62,  60,  62,  64,  60,  72,  64,  70,  61,  62,  60,  60,  59, 
65,  60,  70,  58,  62,  61,  64  lb.,  respectively. 

8.  Counting  8  hr.  to  a  day,  find  the  total  amount  and  the 
average  daily  wages  in  the  following  contractor's  time  sheet  : 

TIME   SHEET   FOR    WEEK   ENDING  JUNE   30 


NAME 

M. 

T. 

W. 

T. 

F. 

s. 

HOURS 

DAYS 

DAILY 
WAGES 

AMOUNT 

C.  E.  Ames 

8 

8 

8 

8 

8 

8 

•SI.  75 

W.  0.  Bye 

9 

10 

9 

10 

10 

8 

2.00 

M.  E.  Carey 

10 

9 

9 

10 

8 

10 

2.00 

W.  D.  Frey 

6 

8 

9 

10 

7 

8 

2.25 

G.  W.  Jones 

10 

10 

10 

8 

10 

8 

2.25 

D.  0.  Munn 

4 

4 

4 

G 

8 

6 

2.50 

E.  H.  Post 

G 

6 

6 

6 

4 

4 

3.00 

L.  C.  Roe 

10 

10 

10 

10 

4 

4 

3.25 

J.  H.  Small 

6 

8 

8 

10 

12 

12 

3.25 

H.  M.  Young 

8 

8 

8 

8 

8 

8 

3.50 

Total 

CHAPTER   IX 

CHECKING  RESULTS 

112.  It  has  been  seen  in  the  preceding  exercises  on  statis- 
tics, time  sheets,  etc.,  that  various  ruled  forms  provide  for  prac- 
tical and  convenient  methods  of  checking  results.     While  it  is 
possible  to  give  a  great  variety  of    these  problems  it  is    also 
necessary  to  give  a  great  many  problems  that  do  not  furnish 
such  a  check. 

113.  It  is  very  important  that  all  results  be   checked.     The 
most  common  methods  of  checking  addition,  subtraction,  and 
division  have  already  been    mentioned.      Multiplication   may 
be  proved   by  dividing   the   product   by  either   factor,  or   as 
explained  on  page  52. 

114.  The  properties  of  9  and  11  may  also  be  applied  to  advan- 
tage in  checking  results,  especially  results  in  multiplication  and 
division. 

PROPERTIES   OF   9   AND   11 

PROPERTIES  OF  9 

115.  Any  number  of  10's  is  equal  to  the  same  number  of  9's 
plus  the  same  number  of  units;  any  number  of  100's  is  equal 
to  the  same  number  of  99's  plus  the  same  number  of  units ; 
any  number  of  1000's  is  equal  to  the  same  number  of  999's 
plus  the  same  number  of  units ;  and  so  on. 

Thus,    10  =  one  9  +  1 ;    40  =  four   9's  +  4  ;     100  =  one  99  +  1 ;    300  = 
three  99's  +  3 ;  500  =  five  99's  +  5. 

116.  Any  number  may  be  resolved  into  one  less  than  as  many 
multiples  of  10  as  it  contains  digits. 

Thus,  946  =  900  +  40  +  6 ;  42175  =  40000  +  2000  +  100  +  70-1-5. 

81 


82  PRACTICAL   BUSINESS   ARITHMETIC 

117.  The  excess  of  9's  in  any  multiple  of  a  power  of  10  mul- 
tiplied by  a  single  digit  is  the  same  as  the  significant  figure  in 
that  number.      Hence, 

The  excess  of  9's  in  any  number  is  equal  to  the  excess  of  9's  in 
the  sum  of  its  digits. 

Thus,  the  excess  of  9's  in  241  =  2  +  4  +  1,  or  7.  The  excess  of  9's  in 
946  —  9  _|_  4  _|_  6,  or  19  ;  but  19  contains  9,  and  the  excess  of  9's  in  19  =  1  + 
9,  or  10;  but  10  contains  9,  and  the  excess  of  9's  in  10  =  1  +  0,  or  1;  the 
excess  of  9's  in  946  is  therefore  shown  to  be  1. 

118.  In  finding  the  excess  of  9's  in  any  number,  omit  all  9's 
and  all  combinations  of  two  or  three  digits  which  it  is  seen  at 
a  glance  will  make  9  or  some  multiple  of  9. 

Thus,  in  finding  the  excess  of  9's  in  9458,  begin  at  the  left,  reject  the 
first  digit  9,  the  sum  of  the  next  two  digits,  9,  and  the  single  8  will  be  the 
excess  of  9's  in  the  entire  number. 

PROPERTIES  OF  11 

119.  Any  number  of  10's  is  equal  to  the  same  number  of  ll's 
minus  the  same  number  of  units;   any  number  of  100's  is  equal 
to  the  same  number  of  99's  plus  the  same  number  of  units  ;  any 
number  of  1000's  is  equal  to  the  same  number  of  1001's  minus 
the  same  number  of  units ;  and  so  on. 

Thus,  40  =  four  ll's  -  4;  500  =  five  99's  +  5;  7000  =  seven  1001's  -  7. 

120.  It  is  therefore  clear  that  even  powers  of  10  are  multiples 
of  11  plus  1  and  odd  powers  of  10  are  multiples  of  11  minus  1. 

Thus,  102  or  100  =  nine  ll's  +  1 ;  103  or  1000  =  ninety-one  ll's  -  1 ;  10* 
or  10,000  =  nine  hundred  nine  ll's  +  1. 

121.  From  the  foregoing  it  is  evident  that : 

The  excess  of  Ifs  in  any  number  is  equal  to  the  sum  of  the  digits 
in  the  odd  places  (increased  by  11  or  a  multiple  of  11  if  necessary} 
minus  the  sum  of  the  digits  in  the  even  places. 

Thus,  the  excess  of  ll's  in  45  is  1  (5  —  4)  ;  the  excess  of  ll's  in  125  is  4 
(5^2  +  1~^0);  the  excess  of  ll's  in  2473  is  9  [14  (11  +  3)  -  7  +  2  (4  -  2) 
=  9]. 


CHECKING   RESULTS  83 


CHECKING  ADDITION  AND  SUBTRACTION 

122.    Examples,     l.    By  casting  out  the  9's,  show  that  the 
sum  of  985,  651,  782,  and  465  is  2833. 

SOLUTION.     The  sum   of  the  digits  in  935  is  17  ;  but  since  17        935  =  g 
contains  9,  find  the  sum  of  the  digits  in  17  and  the  result,  8,  is  the        nr^  __  g 
excess  of  9's  in  the  entire  number.     In  like  manner  find  the  ex- 
cess  of  9's  in  651,  782,  and  465.     Since  935  is  a  multiple  of  9  +  8,        '**' 
651  a  multiple  of  9  +  3,  782  a  multiple  of  9  +  8,  465  a  multiple  of       465  =  6 
9  +  6,  the  sum  of  these  numbers.  2833,  should  equal  a  multiple  of     2833  =  7 
9  +  (8  +  3  +  8  +  6),  or  9  +  25.     25  is  a  multiple  of  9  +  7,  and  2833 
is  a  multiple  of  9  +7  ;   hence,  the  addition  is  probably  correct. 

2.    By  casting  out  the  ll's,  show  that  the  sum  of  648,  217, 
451,  and  688  is  2004. 


SOLUTION.      8-4  +  6-0  =  10,    the  excess  of    ll's    in   648.        648=10 
1+2  -0=8,  the  excess  of  ll's  in  217.     12  (11  +  1)  -5+        217=     8 


4  —  0  =  11  ;  but  11  contains  11,  hence,  the  excess  of  ll's  in  451 

is  0.    8^8  +  6^0=6,  the  excess  of  ll's  in  688.     Since  648  is 

a  multiple  of  11  +  10,  217  a  multiple  of  11  +  8,  451  a  multiple  of        688  =     6 

11,  and  688  a  multiple  of  11  +  6,  the  sum  of  these  numbers,  2004,     2004  =    2 

should  be  a  multiple  of  11  +  (10  +  8  +  6),  or  11  +  24.     24  is  a 

multiple  of  11+2  and  2004  is  a  multiple  of  11  +  2;  hence,  the  addition  is 

probably  correct. 

123.  Subtraction  may  be  proved  either  by  casting  out  the  9's 
or  ll's  in  practically  the  same  manner  as  addition. 

The  difference  between  the  excess  of  9's  or  ll's  in  the  minuend  and  sub- 
trahend should  equal  the  excess  of  9's  or  ll's  in  the  remainder;  or  the  sum 
of  the  excess  of  9's  or  ll's  in  the  subtrahend  and  remainder  should  equal 
the  excess  of  9's  or  ll's  in  the  minuend. 

These  methods  are  but  little  used  for  checking  addition  and  subtraction. 
Addition  is  generally  checked  as  explained  on  page  20,  and  subtraction  as 
explained  on  page  32.  On  the  other  hand,  long  multiplications  and  divi- 
sions are  almost  always  checked  by  applying  the  properties  of  9  or  11. 

CHECKING  MULTIPLICATION  AND  DIVISION 

124.  Examples.     1.   By  casting  out  the  9's  show  that  the 
product  of  64  x  95  is  6080. 

SOLUTION.     The  excess  of  9's  in  95  is  5,  and  in  64,  1.     Since  95  95  =  5 

is  a  multiple  of  9  +  5  and  64  a  multiple  of  9  +  1,  the  product  of  ci  __  i 

64  x  95  should  be  a  multiple  of  9  plus  (1x5).     1  x  5  or  5  equals  ^    " 

the  excess  of  9's  in  6080  ;  hence,  the  work  is  probably  correct.  6080  =  5 


84  PRACTICAL   BUSINESS   ARITHMETIC 

2.  By  casting  out  the  ll's  show  that  the  product  of  46  x  95 
is  4370. 

SOLUTION.     The  excess  of  IPs  in  95  is  7,  and  in  46,  2.     Since          95  —  7 

95  is  a  multiple  of  1  +  17  and  46  a  multiple  of  11  +  2,  the  prod-  tn> o 

uct  of  46  x  95  should  be  a  multiple  of  11  plus  (2  x  7)  or  14;  but 
14  is  a  multiple  of  11  +  3.  Since  the  product  4370  is  a  multiple  of 
11  +  3,  the  work  is  probably  correct. 

125.  Division  may  be  proved  either  by  casting  out  the  9's  or 
ll's  in  practically  the  same  manner  as  multiplication.  The 
excess  of  9's  or  ll's  in  the  quotient  multiplied  by  the  excess 
of  9's  or  ll's  in  the  divisor  should  equal  the  excess  of  9's  or 
ll's  in  the  dividend,  minus  the  excess  of  9's  or  ll's  in  the  re- 
mainder, if  any. 

Casting  out  the  9's  will  not  show  an  error  caused  by  a  transposition  of 
figures;  but  casting  out  the  ll's  will  show  such  an  error.  The  method  of 
casting  out  the  ll's  is  therefore  considered  the  better  proof. 

WRITTEN  EXERCISE 

1.  Determine  without   dividing  whether  $2.64  is  the  quo- 
tient of  $1375.44 -v- 521. 

2.  Determine  without  multiplying  whether  $1807.50  is  the 
product  of  482  times  $3.75. 

3.  Determine  without  adding  whether  4231  is  the  sum  of 
296,  348,  924,  862,  956,  and  845. 

4.  Multiply  34,125  by  729  in  two  lines  of  partial  products 
and  verify  the  work  by  casting  out  the  9's. 

5.  Find  the  cost  of  173,000  shingles  at  $4.27  per  thousand, 
in  two  lines  of  partial  products,  and  verify  the  work  by  casting 
out  the  ll's. 

6.  Find  the  cost  of  126,000  ft.  of  clear  pine  at  $24.60  per 
thousand,  in  two  lines  of  partial  products,  andv  verify  the  work 
by  casting  out  the  9's. 

7.  Find  the  cost  of   2,191,000  ft.  of  flooring  at  $32.08  per 
thousand,  in  two  lines  of  partial  products,  and  verify  the  work 
by  casting  out  the  ll's. 


FRACTIONS 


CHAPTER   X 

DECIMAL  FRACTIONS 
ORAL  EXERCISE 

1.  In  the  number  $7.62  what  figure  stands  for  the  dollars  ? 
the  tenths  of  a  dollar?  the  hundredths  of  a  dollar? 

2.  What  name    is   given   to  the  point  which  separates  the 
whole  number  of  dollars  from  the  part  of  a  dollar  ? 

3.  Read:   3.5  dollars;    3.5ft.;    27.5  lb.;    .7  of  a  dollar;  .5 
of  a  ton;   16.6;   .9;   9.25  dollars;   7.25ft.;   8.75  rd.;   .95  of  a 
dollar ;   .85  of  a  pound  sterling  ;   .57. 

4.  What  is  the  first  place  at  the  right  of  the  -decimal  point 

called  ?  the  second  place  ? 

izD 

5.  In    the    accompanying      B 

diagram  what  part  of  A  is  B  ?  |  \  M  ,  ,<  \  M  |  .( 
What  part  of  B  is  C?    What 
part  of  C  is  D? 

6.  What  part  of  A  is  C? 
What  part  of  A  is  D? 

7.  If  A  is  a  cubic  inch,  what  is  B?   C?  D? 

8.  In  a  pile  of  10,000  bricks  one  brick  is  what  part  of  the 
whole  pile?     10  bricks  is  what  part  of  the  whole  pile?     100 
bricks  is  what  part  of  the  whole  pile?      1000  bricks  is  what 
part  of  the  whole  pile  ? 

9.  How   may    one    tenth  be  written  besides   ^?  one   hun- 
dredth besides  -j-J-^  ?  one  thousandth  besides  I-^QQ  ? 

126.  Units  expressed  by  figures  at  the  right  of  the  decimal 
point  are  called  decimal  units. 

127.  A  number   containing  one    or  more    decimal   units   is 
called  a  decimal  fraction  or  a  decimal. 

85 


86  PRACTICAL   BUSINESS   ARITHMETIC 

NOTATION   AND   NUMERATION 

ORAL  EXERCISE 

1.  Read:   0.7;  0.03  ;  0.25.     How  many  places  must  be  used 
to  express  completely  any  number  of  hundredth^? 

2.  Read:   0.004;  0.025;  0.725.      How  many  places  must  be 
used  to  express  completely  any  number  of  thousandths  ? 

3.  Read:  .0005;  .00007;  .000009;  .0037;  .00045;   .000051; 
.0121;    .00376;    .000218;    .1127;    .01525;     .004531;    .16067. 

4.  How  many  places  must  be  used  to  express  completely  any 
number   of    ten-thousandths?    any    number   of    hundred-thou- 
sandths? any  number  of  millionths? 

128.  In   reading   decimals   pronounce  the  word  and  at  the 
decimal  point  and  omit  it  in  all  other  places. 

Thus,  in  reading  0.605  or  .605  say  six  hundred  five  thousandths  ;  in  reading 
600.005  say  six  hundred  and  jive  thousandths. 

129.  The  relation  of  integers  and  decimals  with  their  increas- 
ing and  decreasing  orders  to  the  left  and  to  the  right  of  the 
decimal  point  is  shown  in  the  following 

NUMERATION  TABLE 

PERIODS  :          Millions          Thousands          Units  Thousandths          Millionths 


ORDERS  :      |      a  J     1  j§     J        !     J 

*&  -— <  r&  &  r-<  <"rt  ^rt  2  ^  'M 

I  -1     "         £2«  ««2l22S 

^  !  I    ill    i  s  5  1 1  1  1    li  = 

O         •'-^  (U         ^  3<£>^(£)S^<--5  <D 

KH^        KHH       MH^QHMH       HfflS 
987,       654,       321.234      567 

130.  Hundredths  are  frequently  referred  to  as  per  cent,  a 
phrase  originally  meaning  by  the  hundred. 

131.  The  symbol  %  stands  for  hundredths  and  is  readier  cent. 
Thus  45%  =  .45 ;  48%  of  a  number  =  .48  of  it. 


DECIMAL   FRACTIONS  87 

ORAL   EXERCISE 

Read : 

1.  0.073.  5.  532.002.  9.  31.08%. 

2.  0.00073.  6.  60.0625.  10.  126.75%. 

3.  3004.025.  7.  63.3125.  11.  2150.1875. 

4.  300.4025.  8.  126.8125.  12.  3165.00625. 

13.  131.3125  T.  15.    A  tax  of  1.0625  mills. 

14.  240. 0125  A.  16.   A  tax  of  9. 1875  mills. 

17.  Read  the  number  in  the  foregoing  numeration  table. 

18.  Read  the  following,  using  the  words  "  per  cent ":   .17; 
28;   .85;  .67;  .425;   .371. 

19.  Read   the    following  as  decimals,  not  using  the  words 
"percent":   25%;   75%;    87%;    621%;   27.15%. 

20.  Read  aloud  the  following  : 

a.  The  value  of  a  pound  sterling  in  United  States  money  is 
$4.8665. 

b.  A   meter    (metric    system    of     measures)    is    equal    to 
39.37079  in.;  a  kilometer,  to  0.62137  mi. 

c.  1  metric  ton  is  equal  to  1.1023  ordinary  tons ;  1.5  metric 
tons  are  equal  to  1.65345  ordinary  tons. 

d.  A  flat   steel   bar  3  in.  wide   and   0.5   in.  thick  weighs 
5.118  Ib. 

e.  The  circumference  of  a  circle  is  3.14159  times  the  length 
of  its  diameter. 

WRITTEN    EXERCISE 

Write  decimally  : 

1.  Five  tenths  ;  fifty  hundredths  ;  five  hundred  thousandths. 

2.  Nine  hundred  and  eleven  ten-thousandths  ;  nine  hundred 
eleven  ten-thousandths ;    five  hundred  and  two   thousandths. 

3.  One    hundred    seventy-four    millionths ;      one    hundred 
seventy-four  million  and  seven  millionths ;  seven  million  and 
one  hundred  seventy-four  millionths. 

4.  Seven  thousand  and  seventy-five  ten-thousandths;    two 
hundred  fifty-seven  ten-millionths ;   two  hundred  and  forty-six 
millionths ;  two  hundred  forty-six  millionths. 


88  PRACTICAL    BUSINESS   ARITHMETIC 

5.  Four  million  ten  thousand  ninety-seven  ten-millionths  ; 
four  million  ten  thousand  and  ninety-seven  ten-mill  ionths;  five 
hundred  millionths;  five  hundred-millionths. 

6.  Six   hundred  six  and   five  thousand   one   hundred-thou- 
sandths;   six  hundred  six  and  fifty-one  hundred-thousandths; 
fifty-six  and  one  hundred  twenty-eight  ten-billionths. 

7.  Seventeen   thousand  and   eighteen    hundred   seventy-six 
millionths;   seventeen  thousand  and  eighteen  hundred  seventy- 
six  ten-thousandths  ;   twenty-one  hundred  sixteen  hundredths. 

132.  In  the  number  2.57  there  are  2  integral  units,  5  tenths 
of  a  unit,  and  7  hundredths  of  a  unit.     In  the  number  2.5700 
there  are  2  integral  units,  5  tenths  of  a  unit,  7  hundredths  of 
a  unit,  0  thousandths  of  a  unit,  and  0  ten-thousandths  of  a  unit. 
2.5700  is  therefore  equal  to  2.57.     That  is, 

Decimal  ciphers  may  be  annexed  to  or  omitted  from  the  right 
of  any  number  without  changing  its  value. 

ORAL   EXERCISE 

Read  the  following  (a)  as  printed  and  (£)  in  their    simplest 
decimal  form  : 

1.  0.700.  3.    16.010.  5.  0.50.  7.    0.7000. 

2.  5.2450.         4.    18.210.  6.  0.00950.  8.    12.9010. 

ADDITION 

ORAL  EXERCISE 

1.  What  is  the  sum  of  0.4,  0.05,  0.0065  ? 

2.  What  is  the  sum  of  0.3,  0.021,  0.008  ? 

3.  Find  the  sum  of  seven  tenths,  forty-four  hundredths,  and 
two  ;   of   four  tenths,  twenty-one    hundredths,  and    six    thou- 
sandths. 

133.  Example.    Find  the  sum  of  12.021,  256.12,  and  27.5. 

SOLUTION.    Write  the  numbers  so  that  their  decimal  points  12.021 

stand  in  the  same  vertical  column.    Units  then  come  under  units,  o^ft  1  9 

" 


tenths  under  tenths,  and  so  on.     Add  as  in  integral  numbers  and 
place  the  decimal  point  in  the,  sum  directly  under  the  decimal 


points  in  the  several  numbers  added.  295.641 


DECIMAL   FRACTIONS  89 

WRITTEN  EXERCISE 

Find  the  sum  of: 

1.  7.5,  165.83,  5.127,  6.0015,  and  71.215. 

2.  257.15,  27.132,  5163,   8.000125,  and  4100.002. 

3.  0.175,  5.0031,  .00127,  70.2116001,  and  21.00725. 

4.  51.6275,  19.071,  0.000075,  21.00167,  and  40,000.01. 

5.  2.02157,  2.1785,  2500.00025,  157.2165,  and  7.0021728. 

6.  Copy,  find  the  totals  as  indicated,  and  check  : 

•$1241.50        $9215.45       $1421.12       $1421.32  ? 

1.52          1275.92  1.46          1618.40  ? 

349.21  3725.41  2.18          1920.41  ? 

2975.47          7286.95  7.96  10.20  ? 

27.14          8276.92  14.21  41.64  ? 

9218.49  7271.44  1240.80  126.18  ? 

5.17  8926.95          7216.80  24.17  ? 

12627.85          8972.76  4.75  240.20  ? 

721.92  7214.25  8.16  960.80  ? 

11.41  8142.76  .47          1860.45  ? 

1.21  8136.14  .92          9270.54  ? 

.72          8435.96  9.26  75.86  ? 

14178.21    7926.14    1490.75      45.95  ? 

2172.14     9214.72     1860.54      75.86  ? 

726.95    1241.16    9265.80      72.18  ? 

85.21     4214.71     625.50    9260.14  ? 

75.92    8726.19     240.75       1.20  ? 

72604.25    2140.12      60.50       7.40  ? 

124.61     7146.14     120.41       8.32  ? 

2114.62     7214.86     4101.08    2860.14 


7.  Find  the  sum  of  twenty-one  hundred  sixty-five  and  one 
hundred  sixty-five  ten-thousandths,  thirty-nine'  and  twelve 
hundred  sixty-five  millionths,  twenty-seven  hundred  thirty- 
six  and  one  millionth,  four  and  six  tenths,  six  hundred  and 
six  thousandths,  and  six  hundred  sixty-five  thousandths. 


90  PRACTICAL   BUSINESS   ARITHMETIC 

SUBTRACTION 

ORAL   EXERCISE 

1.  From  the  sum  of  0.7  and  0.4  take  0.5. 

2.  From  the  sum  of  0.07  and  0.21  take  0.006. 

3.  From  seventy-four  hundredth 8  take  six  thousandths. 

4.  To  the  difference  between  .43  and  .03  add  the  sum  of 
.45  and  .007. 

5.  Goods  on  hand  at  the   beginning   of  a  week,   $24.50; 
goods  purchased  during  the  week,  $35.50;  goods  sold  during 
the  week,  $36 ;  goods  on  hand  at  the  close  of  the  week,  $36.50. 
What  was  the  gain  or  loss  for  the  week  ? 

134.    Example.     From  14.27  take  5.123. 

SOLUTION.     Write  the  numbers  so  that  the  decimal  points  stand         14. 27 
in  the  same  vertical  column.     The  minuend  has  not  as  many  places  5 

as  the  subtrahend  ;  hence  suppose  decimal  orders  to   be  annexed 
until  the  right-hand  figure  is  of  the  same  order,  then  subtract  as 
in  integers   and  place  the  decimal  point  in  the  remainder  directly  under  the 
decimal  points  in  the  numbers  subtracted. 

WRITTEN  EXERCISE 

Find  the  difference  betiveen: 

1.  7.2154  and  2.8576.  5.    9  and  5.2675. 

2.  17.2157  and  1.0002.  6.    16  and  5.0000271. 

3.  1.0005  and  .889755.  7.    .0002  and  .000004. 

4.  $1265.45  and  $87.99.  8.    24.503  and  17.00021. 
9.    The  sum  of  two  numbers  is  166.214.     If  one   of  the 

numbers  is  40.21,  what  is  the  difference  between  the  numbers? 

10.  The    minuend   is    127.006    and    the    remainder    15.494. 
What  is  the  sum  of  the  minuend,  subtrahend,  and  remainder? 

11.  From  the  sum  of  ninety-nine  ten-thousandths,  one  hun- 
dred fifty-one  and  five  thousandths,  two  hundred  fifty-two  and 
twenty-five  millionths,  six  tenths,  and  eighteen  and  one  hun- 
dred seventy-five  thousandths  take  the  sum  of  twelve  hundred 
fifteen  millionths,  and  one  hundred  eighty-eight  thousandths. 


DECIMAL   FRACTIONS  91 

12.  From  the  sum  of  two  hundred  fifty-seven  thousandths 
and  eight  and  one  hundred  twenty-six  millionths  take  the  sum 
of  five  hundred   ten  thousandths  and  two  and  one   hundred 
twenty-four  ten-thousandths. 

13.  A    merchant   had,    at   the   beginning  of  a  year,   goods 
amounting   to   $ 8165. 95.       During    the    year    his    purchases 
amounted  to  15265.90  and  his  sales  to  $9157.65.     At  the  close 
of  the  year  he  took  an  account  of  stock  and  found  that  the 
goods  on  hand  were  worth  $7216.56.     What  was  his  gain  or 
loss  for  the  year? 

14.  A  provision  dealer  had  on  hand  Jan.   1,  goods  worth 
$4127.60.     His  purchases  for  the  year  amounted  to  $4165.95 
and  his  sales  to  $6256.48.     Dec.  31  of  the  same  year  his  in- 
ventory showed  that  the  goods  on  hand  were  worth  $3972.50. 
If  the  amount  paid  for  freight  on  the  goods  bought  amounted 
to  $237.50,  what  was  his  gain  or  loss  on  provisions? 

15.  I  had  on  hand  Jan.  1,  lumber  amounting  to  $4210.60. 
During  the  year  my  purchases  amounted  to  $3126.50,  and  my 
sales  to  $4165.85.     I  lost  by  fire  lumber  valued  at  $506.75,  for 
which    I    received   from  an    insurance    company   $500.     Dec. 
31,  my  inventory  showed  the  lumber  to  be  worth  $5209.08. 
How  much  did  I  gain  or  lose  on  lumber  during  the  year? 

16.  At  the  beginning  of  a  year  my  resources  were  as  follows: 
cash  on  hand,  $1262.50;  goods  in  stock,  $1742.85;    account 
against  A.  M.  Eaton,  $146.50.     At  the  same  time  my  liabili- 
ties were  as  follows:  note  outstanding,  $156.85;  account  in 
favor  of  Robert  Wilson,  $521.22.     During  the  year  I  made  an 
additional  investment  of  $1250.65,  and  withdrew  for  private 
use  $275.     I  sold  for  cash  during  the  year  goods  amounting  to 
$1250.75,  and  bought  for  cash  goods  amounting  to  $530.90  ;   I 
also  paid  Robert  Wilson  $320  to  apply  on  account.     At  the 
close  of  the  year  my  inventory  showed  goods  in  stock  valued  at 
$750.48.     What  was  my  gain  or  loss  for  the  year  and  my  pres- 
ent worth  at  the  close  of  the  year  ? 

Do   not  fail  to  check  all  problems.     No   phase  of  arithmetic  is  more 
important. 


92  PRACTICAL   BUSINESS   ARITHMETIC 

MULTIPLICATION 

ORAL   EXERCISE 

1.  How  many  times  .4  is  4?  .77  is  7.7?  .999  is  9.99? 

2.  44  is  how  many  times  .44?  22  is  how  many  times  .022? 
1  is  how  many  times  .001  ?  .01  is  how  many  times  .0001  ? 

3.  Read  aloud  the  following,  supplying  the  missing  terms  : 
Removing  the  decimal  point   one   place   to   the    right   multi- 
plies  the  value  of  the  decimal  by  -      -   ;  two  places,  —    —  the 
value  by ;  three  places,  -     -  the  value  by  -    — . 

4.  Multiply  12.1252  by  1000  ;  by  100  ;  by  100,000. 

5.  Multiply  $9.375  by  100;  by  10,000 ;  by  100,000. 

6.  Multiply  5. 15  by  10;  by  100  ;  by  1000 ;  by  10,000. 

7.  Multiply  .000016  by  1000;  by  100,000  ;  by  1,000,000. 

8.  Multiply  $67.50  by  10  ;  by  100  ;  by  1000  ;  by  10,000. 

9.  Multiply  .0037  by  10;  by  100;  by  1000;  by  10,000,000. 

10.  What  part  of  1  is  .1  ?  of  7  is  .7?  of  29  is  2.9? 

11.  What  part  of  84  is  .84?  of  129  is  1.29?  of  1275  is  12.75? 

12.  What  part  of  .6  is  .006?  of  .64  is  .0064? 

Read  aloud  the  following,  supplying  the  missing  terms : 

a.  Each  removal  of  the  decimal  point  one  place  to  the  left 
the  value  of  the  decimal  by  10. 

b.  To  divide  a  decimal  by is  to  find  one  tenth  (.1)   of 

it,  or  to it  by  .1. 

13.  Give  a  short  method  for  multiplying  a  number  by  .1 ;  by 
.01;  by  .001;  by  .0001. 

14.  Multiply  .009  by  .1;  by  .01;  by  .001. 

15.  Multiply  217.59  by  .1;  by  .01 ;  by  .001. 

16.  Multiply  54.65  by  .01;  by  .00001;  by  .000001. 

17.  Multiply  2.375  by  .1;  by  .01;  by  .001  ;  by  .0001. 

18.  Multiply  25.215  by  .1;  by  .01;  by  .001;  by  .0001. 

19.  Multiply  2111  by  .01  ;  by  .001  ;  by  .0001 ;  by  .00001. 

20.  Compare    2400  x  $0.06    with    100x24x80.06  or  with 
24x$6. 

21.  Compare  3000  x  612.251  with  1000  x  3  x  612.251,  or  with 
3  x  612251. 


DECIMAL   FRACTIONS  93 

22.  Multiply  21.25  by  2400. 

SOLUTION.     2400  is  24  times  100.     Multiply  by  100  2125  2125 

by  removing  the  decimal  point  two  places  to  the  right.  cy\  04 

The  result  is  2125.     24  times  2125  equals  51,000,  the  -— — - 
required  product. 

In  multiplying  begin  with  either  the  lowest  or  the  4250  8500 

highest  digit  in  the  multiplier  as  shown  in  the  margin.  51000  51000 

23.  Formulate  a  brief  rule  for  multiplying  a  decimal  by  any 
number  of  10's,  100's,  1000's,  etc. 

24.  Find  the  cost  of  : 

a.  500  Ib.  at  18 £      d.    600  Ib.  at  29^.      g.    900  Ib.  at  34^. 

b.  15011).  at  14£       e.    300  Ib.  at  41^.      h.    700  Ib.  at  51  £ 
<?.    200  Ib.  at  26^.       /.    400  Ib.  at  12^.    i.     1400  Ib.  at  5£ 

135.   Examples,     i.   Multiply  41.127  by  4. 

SOLUTION.  41.127  is  equal  to  41,127  thousandths.  41,127  thou-  41.127 
sandths  multiplied  by  4  equals  161,508  thousandths,  or  164.508.  That  4 

is,  thousandths  multiplied  by  a  whole  number  must  equal  thousandths.    1(54.508 

2.    Multiply  41.127  by  .04. 

SOLUTION.     The  multiplier,  .04,  is  equal  to  4  times  .01 ;  therefore,  41.127 

multiply  by  4  and  by  .01.     Multiplying  by  4,  as  in  problem  1,  the  Q^ 

result  is  164.508.     Multiplying  by  .01,  by  simply  moving  the  decimal  ' 

point  in  the  product  two  places  to  the  left,  the  result  is  1.64508.  l-^oUc 

It  will  be  seen  that  the  number  of  decimal  places  in  the  product 
is  equal  to  the  decimal  places  in  the  multiplicand  and  multiplier. 

It  should  not  be  necessary  to  memorize  the  above  rule.  The  student 
should  know  at  a  glance  that  the  product  of  tenths  and  tenths  is  hundredths, 
of  tenths  and  huudredths  is  thousandths,  and  so  on. 

ORAL    EXERCISE 

1.  In  multiplying  24.05  by  3.14  can  you  tell  before  multiply- 
ing how  many  integral  places  there  will  be  in  the  product  ? 
how  many  decimal  places  ?     Explain. 

2.  How  many  integral  places  will  there  be  in  each  of  the  fol- 
lowing  products  :      2.5x4.015?      27.51x3.1416?     321.1  x 
201.51?  1.421x42.267?  126.5  x  .01?  1020x5.01?  .105x6? 
2.41  x  10.05  ?     How  many  decimal  places  will  there  be  in  each 
of  the  above  products  ? 


94 


PEACTICAL   BUSINESS   AEITHMETIC 


3.  What  are  400  bbl.  of  apples  worth  at  $2.12  per  barrel? 
at  fl. 27-|-  per  barrel? 

4.  I  bought  60  Ib.  of  sugar  at  $0.04J  and  gave  in  payment  a 
five-dollar  bill.     How  much  change  should  I  receive? 

5.  A  and  B  are  partners  in  a  manufacturing  business,  A  re- 
ceiving 52  %  and  B  48  %  of  the  yearly  profits.     The  profits  for 
a  certain  year  are  $5000.     Of  this  sum  how  much  should  A  and 
B,  respectively,  receive  ? 


7.  2.531x31000. 

8.  .1724x18000. 

9.  .15539  x  2002. 


WRITTEN  EXERCISES 

Find  the  product  of: 

1.  3.121  x  152.  4.  12.14  x  265. 

2.  3121  x  .152.  5.  9.004  x  .021. 

3.  31.21  x  15.2.  6.  .3121  x  .0152. 

10.  A  man  owned  75%  of  a  gold  mine  and  sold  50%  of  his 
share.     What  is  the  remainder  worth  if  the  value  of  the  whole 
mine  is  $425,000? 

11.  A  man  bought  a  farm  of  240  A.  at  $137.50  per  acre. 
He  sold  75%  of  it  at  $150  per  acre,  and  the  remainder  at  $175 
per  acre.     What  was  his  gain  ? 

12.  Copy  and   complete   the  following   table   of  statistics. 
Check  the  results.     (The  total  yield  multiplied  by  the  price 
per  bushel  should  equal  the  total  valuation.) 

LARGEST  WHEAT-GROWING  STATES  IN  A  RECENT  YEAR 


STATE 

YIELD  IN  BUSHELS 

FARM  PRICK 
i'EK  BUSHEL 

FARM  VALUATION 

Minnesota 
Kansas 
North  Dakota 
South  Dakota 

68,344,256 
65,019,471 
53,892,193 
31,556,784 

92.4^ 
92.4^ 
92.4^ 
92.  4  J* 

Total 

13-15.    Make  and  solve  three  self-checking  problems  in  multi- 
plication of  decimals. 


DECIMAL   FRACTIONS  95 

DIVISION 

ORAL   EXERCISE 

1.  Divide  by  8  :  64  ft.,  .64,  .064,  6.4. 

2.  Divide  by  9 :  63  in.,  .63,  .063,  6.3. 

3.  Divide  by  16:  $640,  -16.40,  6.4,  .64,  .064. 

4.  Divide  by  15:  $15.75,  $7.50,  $0.75,  30.45,  3.045,  .3045. 

5.  Divide  337.5  by  45. 

7.5 
45)337.5 

315     =  45  times  7 
22.5  undivided 
22.5  =45  times  .5 
CHECK.     45  times  7.5  =  337.5 ;  hence,  the  work  is  probably  correct. 

136.  In  the  above  exercise  it  is  clear  that  when  the  divisor  is 
an  integer,  each  quotient  figure  is  of  the  same  order  of  units  as  the 
right-hand  figure  of  the  partial  dividend  used  to  obtain  it. 

ORAL  EXERCISE 

1.  500  is  how  many  times  50?     $75  is  how  many  times 
$7.50? 

2.  Divide  50  by  5 ;   500  by  50.     How  do    the    quotients 
compare  ? 

3.  Divide  7.50  by  15  ;  $75  by  150.     How  do  the  quotients 
compare  ? 

4.  720  is  how  many  times  72  ?     9  is  how  many  times  .9? 

5.  Divide  720  by  9;   72  by  .9;   7.2  by  .09;   .72  by  .009. 

137.  It  has  been  seen  that   multiplying  both  dividend  and 
divisor  by  the  same  number  does  not  change  the  quotient. 

138.  Therefore,  to  divide  decimals  when  the  divisor  is  not  an 
integer : 

Multiply  both  dividend  and  divisor  by  the  power  of  10  that 
shall  make  the  divisor  an  integer,  and  divide  as  in  United  States 
money. 


96 


PRACTICAL   BUSINESS   ARITHMETIC 


139.    Divide  0.3375  by  0.45. 

.3375  -r-  .45  =  33.75  -H  45.     33.75  +  45  =  .7,  with  a  remainder  of  .  75 

2.25.     2.25  -T-  45  =  .05.     The  quotient  is  therefore  .75.  45')8d  'J  " 

Observe  that  £/ie  divisor  may  always  be  made  an  integer  if  the  01  "r 

decimal  point  in  the  dividend  is  carried  to  the  right  as  many  places  —       •  • 

as  there  are  decimal  places  in  the  divisor. 

Should  there  be   a  remainder  after  using  all  the  decimal  ^  ^5 

places  in  the  dividend,  annex  decimal  ciphers  and  continue  the  division 
as  far  as  is  desired. 


ORAL    EXERCISE 


Divide  : 

1. 

1  by  1. 

2. 

1  by  .1. 

3. 

1  by  10. 

4. 

.1  by  .1. 

5. 

1  by  .01. 

6. 

1  by  100. 

7. 

1  by  .001. 

8. 

.10  by  .10. 

9. 

.01  b}  .01. 

10. 

1  by  1000. 

11. 

1  by  .0001. 

12. 

1  by  10,000. 

13. 

1  by  .00001. 

14. 

.001  by  .001. 

15. 

1  by  100,000. 

16. 

1  by  .000001. 

17. 

.0001  by  .0001. 

18. 

.00001  by  .00001. 

19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32 
33. 
34. 
35. 
36. 


WRITTEN  EXERCISE 

Divide  : 

1.  5842  by  .046.  6.  2200  by  .44. 

2.  2.592  by  .108.  7.  231.6  by  579. 

3.  1.750  by  8750.  8.  950  by  19,000. 


33  by  .11. 
33  by  110. 
.33  by  .11. 
3.3  by  1.1. 
.0001  by  1. 
33  by  .011. 
33  by  1100. 
.0001  by  .1. 
3300  by  .11. 
330  by  .011. 
33  by  .0011. 
33  by  11000. 
.0001  by  .01. 
.033  by  .011. 
.0001  by  .001. 
.0033  by  .0011. 
.0001  by  .0001. 
.0001  by  .00001, 


11.  16  by  .0064. 

12.  1.86  by  31,000. 

13.  1600  by  64,000. 


4.  .00338  by  .013.  9.    81.972  by  .00009.    14.    .0004  by  20,000. 

5.  1.728  by. 0024.  10.  115.814  by  .00079.    15.    100  by  .000001. 


DECIMAL   FRACTIONS 


97 


Find  the  sum  of  the  quotients  : 


16. 

8.1  -h.9. 
81  -S-.09. 
8.1  -.09. 
.81-900. 
.0081-9. 
8.1  -=-900. 
810  -.009. 
.  0081  -r-  9000. 
81000  -.009. 
81  -.000009. 
8100-90000. 
.00081-5-90000. 

19. 

8.8-2.2. 
.88  -i-  .22. 

88  -.0022. 

8.8-2200. 
880  -=-2200. 
8.8-2.200. 
880  -.2200. 
8800  -f-  2200. 
880  +  22000. 
880^.00022. 
88000  -.0022. 
88000  -.00022. 


17. 

72-8. 
72+. 8. 
7.2  +  . 8. 

72 -.08. 
.72 -.08. 
72 -.008. 
72  -  8000. 
72 -.0008. 
.072 -.008. 
72 -.00008. 
.0072 -.0008. 
.00072 -.00008. 

20. 

17  +  68. 
1.7  +  6.8. 

.17-?-. 68. 
1.7  +  680. 

170  -  680. 
.017 -.068. 
1.7-68000. 
1700-6800. 
1700  -  68000. 
.0017 -=-.0068. 
. 00017  H-. 00068. 
.000017-^.000068. 


18. 

125  -  250. 
12.5-2.5. 
1.25  +  2.5. 
12.5-250. 
125  +  2500. 
.125 -.025. 
12500 -.25. 
125  -  25000. 
12500 -.025. 
125  +  250000. 
.125 +  .00025. 
12500  -=-  .0025. 

21. 

36 -.072. 
3.6 -.072. 
.36 +  .072. 
360 -.072. 
.036 -.072. 
3.6-72000. 
36  -=-  720000. 
360 -.00072. 
3600 -.0072. 
.0036 -=-.0072. 
3.6 -.000072. 
. 00036 -T-. 00072, 


22.  The  product  of  two  numbers  is  0.00025.     If  one  of  the 
numbers  is  0.0025,  what  is  the  other? 

23.  A  retailer  bought  450  yd.   of  cloth    for   $1237.50   and 
sold  it  at  $3.25  per  yard.     How  much  did  he  gain  per  yard? 

24.  A  drover  bought  a  flock  of  sheep  at  the  rate  of  $3.30 
per  head.     He  sold  them  at  a  profit   of  $0.20  per  head  and 
received   $700.       How    many    sheep  were    there    in  the  flock 
and  what  was  his  gain  ? 


98 


PRACTICAL   BUSINESS    ARITHMETIC 


25.    Copy   and   complete  the    following   table.      Check   the 
results. 

LARGEST  OAT-GROWING  STATES  IN  A  RECENT  YEAR 


STATE 

YIELD  IN  BUSHELS 

FARM  PKK.-B 
PER  BUSHEL 

FARM  VALUATION 

Illinois 
Iowa 
Wisconsin 
Minnesota 

31  t 
31  f 
31? 

31? 

36,376,005 
37,920,192 
26,887,699 
26,405,335 

12 
00 

65 
93 

Total 

26-28.    Make    and    solve    three   self-checking    problems   in 
division   of  decimals. 

DIVIDING   BY   POWERS   AND   MULTIPLES   OF   TEN 

ORAL   EXERCISE 

1.  6.4  is  what  part  of  64?     $0.17  is  what  part  of  $1.70? 

2.  Compare  (as  in  problem  1)  $240.60  with  $24,060;  17.75 
ft.  with  1775  ft. 

3.  Compare  (as  in  problem  1)  .1  with  1;   .01  with  1;   .001 
with  1  ;  .0001  with  1. 

4.  Read  aloud  the  following,  supplying  the  missing  terms  : 
Removing  the    decimal  -  place    to    the   -    divides   the 
value  of  the  decimal  by  10  ;  two  places,  -  the  value  of  the 
decimal  by  -  ;  three  places,  -  the  value  of  the  decimal 

by  -  .  ' 

5.  Compare  the  quotient  of    28  -4-  .7  with  the   quotient   of 

.7  with  the  quotient  of 


.7  x  10  ;  the  quotient  of  28 


28  x  10 
280-7. 

6.  Compare  the  quotient  of  16.4  —  40  with  the  quotient  of 
16.4  +  10  -r-40-v-lO;  the  quotient  of  16.4  —  40  with  the  quotient 
of  1.64  -r-  4.  What  is  the  quotient  of  56.77  divided  by  7000? 

SOLUTION.     Removing  the   decimal  point  three  places  to   the  nnctl 

left  and  dropping  the  ciphers  of  the  divisor  is  equivalent  to  dividing 
both  dividend  and  divisor  by  1000  and  does  not  change  the  value      0*  05677 
of  the  quotient. 


DECIMAL   FRACTIONS  99 

BUYING  AND  SELLING  BY  THE  HUNDRED 
ORAL  EXERCISE 

1.  Compare  460  -4- 100  x  $2  with  4.60  x  12. 

2.  Find   the  cost  of  450   Ib.  of  guano  at  $ 4  per  cwt. 

3.  Find  the  cost  of  600  Ib.  of  wire  nails  at  34^  per  cwt. 

4.  Find  the  cost  of  4950  paving  stones  at  1 8  per  C. 

SOLUTION.  C  stands  for  100.  4950  paving  stones  are  49.5  times 
100  paving  stones.  Since  1  hundred  paving  stones  cost  $8,  49.5 
hundred  paving  stones  will  cost  49.5  times  $8,  or  $396.  .  396.0 

WRITTEN    EXERCISE 
Find  the  cost : 


PRICE  PER 

PRICE  PER 

QUANTITY 

HUNDREDWEIGHT 

QUANTITY 

HUNDREDWEIGHT 

i.    450  Ib. 

55? 

5.     1600  Ib. 

71/f 

2.    510  Ib. 

77^ 

6.    2600  Ib. 

15? 

3.    640  Ib. 

60? 

7.    4900  Ib. 

70? 

4.    330  Ib. 

56^ 

8.    3100  Ib. 

88? 

BUYING  AND  SELLING  BY  THE  THOUSAND 

ORAL  EXERCISE 


1.  Compare  3500  -+- 1000  x  19  with  3.500  x  19. 

2.  Compare  12200  -*- 1000  x  15  with  12.2  x  $5. 

3.  Find  the  cost  of  7150  feet  of  lumber  at  $11  per  M. 

SOLUTION.     M  stands  for  thousand.     7150  feet  are  7.15  times  l»lu 

1000  feet.    Since  1  thousand  feet  of  lumber  cost  $11,  7.15  thousand  11 

feet  will  cost  7.15  times  11,  or  $78.65.  78765 

Find  the  cost  of: 

4.  8500  tiles  at  $8  per  M ;  at  $9  per  M. 

5.  4500  bricks  at  $6  per  M  ;  at  $7  per  M. 

6.  7500  shingles  at  $12  per  M  ;  at  $14  per  M. 

7.  3200  ft.  lumber  at  $14  per  M ;  at  $12  per  M. 

8.  15,OQO  ft.  lumber  at  $11  per  M  ;   at  $12  per  M. 

9.  12,000  ft.  lumber  at  $16  per  M  ;  at  $15  per  M. 


100 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 

1.  Find  the  cost  of  17,500  shingles  at  $4  per  M. 

2.  What  is  the  cost  of  2700  envelopes  at  $2.25  per  M  ? 

3.  Find  the  cost  of  27,560  feet  of  oak  lumber  at  $21  per  M. 

4.  Find  the  total  cost  of  : 

275  Ib.  nails  at  $3.50  per  cwt. 
750  Ib.  wire  at  $3.75  per  cwt. 
750  Ib.  guano  at  $4.75  per  cwt. 


125  bolts  at  12.75  per  C. 
750  bolts  at  $3.50  per  C. 
450  fence  posts  at  $6  per  C. 

5.  Find  the  total  cost  of  : 
7600  shingles  at  $4  per  M. 
14,400  ft.  plank  at  $9  per  M. 
24,560  bricks  at  $3.50  per  M. 

6.  Find  the  total  cost  of  : 
760  Ib.  bran  at  $.60  per  cwt. 
5875  Ib.  bran  at  $.70  per  cwt. 


9000  tiles  at  $9.375  per  M. 
2320  ft.  lumber  at  $23  per  M. 
1,270,500  bricks  at  $6.75  per  M. 


4275  Ib.  meal  at  $1.10  per  cwt. 
5600  Ib.  feed  at  $1.10  per  cwt. 
5970  Ib.  meal  at  $1.12  per  cwt.    500  Ib.  oatmeal  at  $2.50  per  cwt. 

7.   Find  the  total  freight  on  : 
8000  Ib.  oil  at  100  per  cwt. 
1500  Ib.  fish  at  58^  per  cwt. 


5100  Ib.  salt  at  73^  per  cwt. 


4950  Ib.  ale  at  52^  per  cwt. 
9900  Ib.  beef  at  72^  per  cwt. 
4950  Ib.  pork  at  57^  per  cwt. 


8.    Find  the  amount  of  the  following  bill  : 


SBangor, 


1Q 


,   &  id  'rid  fe  &  Qo. 


.Tg/vw.g  \5~  /•  a-f^ 


/  2.  frt  rt 


DECIMAL   FRACTIONS 


101 


140.  The  accompanying  illustration  shows  the  three  dials  of 
a  gas  meter.  Each  division  on  the  dial 
at  the  right  denotes  100  cu.  ft.  of  gas 
consumed  ;  each  division  on  the  center 
dial  1000  cu.  ft.  ;  and  each  division  on 
the  dial  at  the  left  10,000  cu.  ft.  The 
dials  are  read  from  left  to  right  by  simply 
taking  the  figures  which  the  hands  have 
just  passed  and  adding  two  ciphers  to  them. 

Thus,  the  above  dial  registers  20,000  cu.  ft.  +  5000  cu.  ft.  +  700  cu.  ft. 
=  25,700  cu.  ft. ;  but  it  is  only  necessary  to  write  257  (2,  5,  7)  and  add 
two  ciphers  to  get  this  result. 

WRITTEN  EXERCISE 

1.  Read  the  accompanying  meters  and  find  the  cost  of  the  gas 
consumed  during  the  period  Jan.  1  to  Feb.  1 

at  11.20  per  1000  cu.  ft. 

2.  The  following  is  the  number  of  cubic 
feet  of  gas  used  in  a  residence  for  the  six 
months    ending    July    1  :     January,    2900 ; 
February,  3200 ;  March,  3700 ;  April,  2900  ; 
May,  2700;  June,  1200.     Find  the  total  gas 
bill  for  the  six  months  at  $0.90  per  1000 
cu.  ft. 

3.  Assuming  that  gas  is  worth  80.95  per  1000  cu.  ft.,  find 
the  amount  of  the  following  bill,  less 


Feb.  1,  1906 


To  THE  BOSTON  GAS  AND  ELECTRIC  LIGHT  Co.,  Dr. 


For  Gas  supplied  by  meter 

7-2-/QQ  cu.  ft.  as  shown  by  Meter  Dial 
/  /*(*  00  cu.  ft.  as  shown  by  Meter  Dial 
TOO  cu.  ft.  at  $1 .00  per  1 000  cu.  ft. 


Discount  of  10%  allowed  if 
paid  on  or  before 


102  PRACTICAL   BUSINESS   ARITHMETIC 

BUYING  AND  SELLING  BY  THE  TON  OF  2000  POUNDS 

ORAL  EXERCISE 


1.  Compare  8000  -H  2000  x  8  with  8000  -f-  1000  x  4. 

2.  Compare  7000  -=-  2000  x  18  with  7x9. 

3.  Find  the  cost  of  4250  Ib.  coal  at  1 8  per  ton. 

SOLUTION.     4250  Ib.  is  4.25  times  1000  Ib.     If  the  cost  of  2  thou-          4.25 
sand  pounds  is  $8,  the  cost  of  1  thousand  pounds  is  .$4.     Since  1 
thousand  pounds  of  coal  cost  $4,  4.25  thousand  pounds  will  cost  4.25 
times  $4,  or  $17.  17.00 

WRITTEN  EXERCISE 

1.    At  $9  per  ton,  find  the  cost  of  the  hay  in  the  following 
weigh  ticket.     Also  find  the  cost  at  18.75  per  ton. 


SCALES  OF  E.  H.  ROBINSON  &  CO. 

No.^L£22  Clyde,  N.Y.. 

Load  of 


From          C^-ts^?lL~  To 


Gross  weight     /^  ^  /  V      Ib. 

Tare      /  <T  &  0      Ib. 

Net  weight    .2-&^4~0  *  Ib. 


Weigher 


2.    At  87.50  per  ton  find  the  cost  of  the  coal   in    the    fol- 
lowing weigh  ticket.     Also  find  the  cost  at  $6.95  per  ton. 


WELLINGTON  -WILD  COAL  CO. 

726  Main  S/rce/.  Rochester,  N.Y. 


No.: 


l^fs?        If, 


TVyiimfar  S/fy^e?^?^?^-.  KeceiW  fy    C. '.  .7)1 .   1?Y>^. 


DECIMAL   FRACTIONS 


103 


of 


3.  What  will  8650  Ib.  of  hay  cost  at  112  per  ton? 

4.  Find  the  cost  of  2150  Ib.  of  coal  at    1  6    per    ton. 

5.  At    $32    per   ton,    what   is    the    cost   of    26,480    Ib. 
phosphate  ? 

6.  Find  the  cost  of  54,260  pounds  of  coal  at  $5.80  per  ton. 

7.  Find  the  cost  of  12  loads  of  coal  weighing  4100,  3900, 
4306,  4100,  4060,  4300,  3286,  3980,  3850,  4130,  3700,  3950  Ib. 
net,  at  $5.20  per  ton. 

8.  Find  the  total  cost  of  :  5265  Ib.  hard  coal  at  $8.40  per  ton  ; 
12,200  Ib.  soft  coal  at  $3  per  ton;  8275  Ib.  cannel  coal  at  $11.  75 
per  ton;  34,160  Ib.  egg  coal  at  $6.20  per  ton;   12,275  Ib.  nut 
coal  at  $5.75  per  ton;  8753  Ib.  grate  coal  at  $5.80  per  ton; 
24,160  Ib.  stove  coal  at  $6.50  per  ton. 

9.  During  the  month  of  January,  in  a  recent  year,  there  were 
consumed  in  a  manufacturing  plant  72  loads  of  coal  weighing  as 
follows:    6100,    6500,    6700,    6840,    7210,    6680,    7250,    8400, 
6100,  6100,  6250,  6380,  6480,  6300,   6500, 

6410,  6570,  6480,  6240,  6370,  6430,   6480, 

7620,  7240,  7110,  7220,  7420,  7480,   6390, 

6900,  6270,  6280,  6290,  6270,  6390,   6420, 

6300,  6120,  6430,  6430,  8100,  6100,   6200, 

6170,  6240,  6390,  6140,  6240,  7190,  7240,    7140,    7200,   6340, 

8420,    6310,    7420,    6120   Ib.    net.      Find   the   cost   at   $5.87^ 

per  ton. 

WRITTEN  REVIEW  EXERCISE 

1.  Of  what  number  is  25.56  both  the  divisor  and  quotient? 

2.  The  sum  of  the  divisor  and  quotient  is  414.06.     If  the 
divisor  is  .6,  what  is  the  dividend? 

3.  In  what  time  will  3  boys  at  $  .75  per  day  earn  as  much 
as  2  men  earn  in  75  da.  at  $2.25  per  day? 

4.  A  merchant  sold  a  quantity  of  flour  for  $370  and  realized 
a  gain  of  $34.     If  the  selling  price  was  $7.40  per  barrel,  what 
was  the  cost  per  barrel? 


6410,    6370, 
7400,    7580, 


6160, 

6300, 

6100,    6250,   6250, 

6120,    6120,    6200, 

6310,    6204,    6160, 


104  PRACTICAL  BUSINESS  ARITHMETIC 

5.  What    number  is  that  which  is  165  times  as  great  as 
82.5? 

6.  If  450  bbl.   of  beef   sold  for  85872.50,  what  was  the 
selling  price  per  hundred  barrels? 

7.  What  will  be  the  cost,  at  15^  per  yard,  of  a  paper  border 
for  a  room  8  yd.  wide  and  12  yd.  long? 

8.  If  .25  be  added  to  a  certain  number,  15  may  be  sub- 
tracted from  it  75  times.      What  is  the  number? 

9.  Wood  costing  $3.50  per  cord  is  sold  for  $4.10  per  cord. 
How  many  cords  must  be  handled  to  gain  $240? 

10.  Find  the  cost  of  8  bbl.  of  pork  weighing  280,  281,  286, 
290,  285,  277,  285,  and   290   Ib.   net,  at   $8.50   per   hundred 
pounds. 

11.  A  flock  of  200  sheep  was  bought  for  $700.     10  of  the 
sheep  died,  and  the  remainder  of  the  flock  was  sold  at  $3.95  per 
head.     What  was  the  gain  or  loss  ? 

12.  A  hardware  merchant  had  .5  of  his  capital  invested  in 
hardware  stock,  .25  of  it  invested  in  government  bonds,  and  the 
remainder,  $4896.25,  on  deposit  in  City  National  Bank.     What 
was  his  entire  capital  ? 

13.  A,  B,  and  C  bought  a  stock  of  goods  for  $7500,  A  con- 
tributing $2500,  B  $3000,  and  C  the  remainder.     They  sold  the 
goods  for  $8400  and  divided  the  profits  equally.     How  much 
of  the  $8400  should  A,  B,  and  C,  respectively,  receive? 

14.  A,  B,  and  C   unite   in  forming  a  manufacturing  estab- 
lishment.    A    invests   .4   of   the   entire   money   put   into    the 
business;    B,    .3;    C,   the  remainder,   $4500.     What  was  the 
total  amount  invested,  and  what  was  A's  and  B's  investment, 
respectively  ? 

15.  A  fails  in  business.     The  excess  of  his  liabilities  over 
resources  is  $  7500.     It  is  found  that  he  can  pay  his  creditors 
but  $.25  on  the  dollar.     B  is  given  $750  in  payment  for  the 
amount  owed  him.     What  was  the  full  amount  of  A's  indebted- 
ness, and  how  much  did  he  owe  B? 


DECIMAL   FRACTIONS  105 

16.  What  is  the  total  freight  on  12,250  Ib.  of  hardware  at 
$.65  per  hundredweight  and  15,670  Ib.  of  hardware  at  $.60 
per  hundredweight? 

17.  A  merchant  bought  250  yd.  of  cloth  at  $3.50  per  yard, 
and  150  yd.  at  $4.25.     At  what  average  price  per  yard  should 
the  whole  be  sold  to  realize  an  average  profit  of  $1  per  yard? 

18.  What  is  the  cost  of  25  bbl.  of  sugar  containing  312,  304, 
309,  317,  330,  325,  315,  318,  317,  305,  319,  320,  325,  330,  335, 
330,  325,  315,  315,  320,  320,  330,  330,  315,  315  Ib.  net,  at  5f  ^ 
per  pound  ? 

19.  A  received  $1088  from  the  sale  of  his  barley  crop.     If  he 
received  $0.85  per  bushel  for  the  barley  and  his  farm  produced 
an  average  of  32  bu.  to  the  acre,  how  many  acres  did  it  take 
to  produce  the  barley? 

20.  A  shoe  manufacturing  pay  roll  shows  that  40  hands  are 
employed  at  $1.45  per  day,  50  hands  at  $1.40  per  day,  10  hands 
at  $3  per  day,  40  hands  at  $2.50  per  day,  and  5  hands  at  $8 
per  day.     Find  the  average  daily  wages. 

21.  A    hardware    merchant    found  that  his  stock  of  goods, 
Jan.  1,  amounted  to  $34,350.65.      During  the  year  he  bought 
goods  amounting  to  $211,165.45,  and  sold  goods  amounting  to 
$220,540.45.      Dec.  31,  he  took  an  account  of  stock  and  found 
that  the  goods  on  hand  at  cost  prices  were  worth  $81,275.64. 
What  was  his  gain  or  loss  for  the  year? 

22.  Without  copying  the  following  figures,  find  (a)  the  sum 
of  each  line,  and  (5)  the  sum  of  each  column.     Prove  the  work 
by  adding  the  line  totals  and  comparing  the  sum  with  the  sum 
of  the  column  totals. 


17.035 

18.0135 

186.02 

126.42 

6.009 

8.005 

5.07 

142.004 

.0634 

3.14 

32.972 

18.0981 

165r42 

1.7538 

9.314 

126.83 

4.931 

.628 

6.75 

.048 

95.16 

6.815 

.8467 

8.41 

.062 

101.215 

21.214 

21.221 

2.61 

18.f)41 

106  PRACTICAL   BUSINESS   ARITHMETIC 

23.    Copy  and  find  the  amount  of  the  following  bill 


of  IT*  Utt*  Upton  &  Co* 


Ccrms 


2-600       7000 


^_  /?         ,  .  . 

^J-^L^-g^f^L^y 


24.    Find  the  cost,  at  112.75  per  ton,  of  the  hay  in  the  follow- 
ing weigh  ticket.     Also  find  the  cost  at  $10.75  per  ton. 


SCALES  OF  E.  H.  ROBINSON  &  CO. 

C&de,  N.Y.,Z 


From. 


Load  of. 


Gross  weight. 

Tare. 

Net  weight. 


Weigher 


25.  Find  the  cost  at  $14.75  per  ton  of  six  loads  of  hay,  the 
gross  weights  and  tares  of  which  were  as  follows :  4920  — 
1848,  4810-1850,  5220-1960,  5820-2140,  4980-1920, 
4910  -  1980  lb. 


CHAPTER   XI 

FACTORS,    DIVISORS,    AND    MULTIPLES 
FACTOKS 

ORAL   EXERCISE 

1.  Name  two  factors  of  63  ;  of  88  ;  of  144  ;  of  128. 

2.  What  are  the  factors  of  49?  of  77?  of  35?  of  21? 

3.  Name  three  factors  of  45 ;   of  66 ;  of  24 ;   of  60 ;  of  80. 

4.  Name  a  factor  that  is  common  to  35  and  77;  36,  63,  and  81. 

5.  Name  three  factors  that  are  common  to  30,  60,  and  210. 

6.  Which  of  the  following  numbers  have  no  factors  except 
itself  and  one  ?     11,  27,  15,  37,  49,  62,  73,  81,  23. 

141.  An  even  number  is  an  integer  of  which  two  is  a  factor. 
An  odd  number  is  an  integer  of  which  two  is  not  a  factor. 
A  prime  number  is  a  number  that  has  no  integral  factor  except 
itself  and  one.  A  composite  number  is  a  number  that  has  one 
or  more  integral  factors  besides  itself  and  one. 

Numbers  are  mutually  prime  when  they  have  no  common  factor  greater 
than  one. 

WRITTEN   EXERCISE 

1.  Make  a  list  of  all  the  odd  numbers  from  1  to  100  in- 
clusive;  of  all  the  prime  numbers;  of  all  the  even  numbers; 
of  all  the  composite  numbers. 

ORAL   EXERCISE 

1.  Is  2  a  factor  of  28  ?  of  125  ?  of  42  ?    of  49  ?     By  what 
means  do  you  readily  determine  this  ? 

2.  Is  5  a  factor  of  125  ?  of  170  ?  of  224  ?  of  1255  ?  of  1056  ? 
By  what  means  do  you  readily  determine  this  ? 

3.  When  is  a  number  divisible  by  10?  by  3  ?  by  9  ? 

107 


108  PRACTICAL    BUSINESS   ARITHMETIC 


TESTS  OF  DIVISIBILITY  OF  NUMBERS 

142.    A  number  is  divisible  by: 

1.  Two,  when  it  is  even,  or  when  it  ends  with  0,  2,  4,  6,  or  8. 

2.  Three,  when  the  sum  of  its  digits  is  divisible  by  3. 

3.  Four,  when  the  number  expressed  by  its  two  right-hand  figures  is 
divisible  by  4. 

4.  Five,  when  it  ends  with  0  or  5. 

5.  Six,  when  it  is  even  and  the  sum  of  its  digits  is  divisible  by  3. 

6.  Eight,  when   the    number  expressed   by  the   last   three    right-hand 
figures  is  divisible  by  8. 

7.  Nine,  when  the  sum  of  its  digits  is  divisible  by  9. 

8.  Ten,  when  its  right-hand  figure  is  a  cipher. 

ORAL  EXERCISE 

Name  one  or  more  factors  of  each  of  the  following  numbers: 


l.  184. 
2.  2781. 
3.  1449. 
4.  638172. 

5.  6984. 
6.  2750. 
7.  8975. 
8.  71168. 

9.  51625. 
10.  83870. 
11.  13599. 
12.  123125. 

13.  14128. 
14.  66438. 
15.  31284. 
16.  17375. 

FACTORING 

143.  Factoring  is  the  process  of  separating  a  number  into  its 
factors. 

144.  Example.    Find  the  prime  factors  of  780. 

780 

SOLUTION.  Since  the  number  ends  in  a  cipher,  divide  it  by  the  prime 
factor  5 ;  since  the  resulting  quotient  is  an  even  number,  divide  it  by  2. 
Since  78  is  an  even  number,  divide  it  by  2  ;  since  the  sum  of  the  digits 
in  the  resulting  quotient  is  divisible  by  3,  divide  by  3.  The  prime 
factors  are  then  found  to  be  5,  2,  2,  3,  and  13. 


IT)!, 


TS 
39 


13 

WRITTEN   EXERCISE 

Find  the  prime  factors  of: 

1.  112.   4.  786.  7.  968.  10.  408.  13.  2718.  16.  6900. 

2.  126.   5.  392,  8.  689.  11.  650.  14.  3240.  17.  2064. 

3.  288.   6.  315.  9.  1098.  12.  762.  15.  3205.  18.  7400. 


FACTOKS,   DIVISORS,   AND   MULTIPLES  109 

CANCELLATION 
ORAL  EXERCISE 
1.    (4  x  15)  -  (4  x  3)  =  15  -f-  3.     Why  ? 


2.    Divide  2x5x7  by  5x2;  8x7x5  by  .5x2x7. 
3    3  x7  x8=  ?      5x2x8x3=  ?        2x9x7x5     9 

7x3  2x8x3  5x7x2x3 

4.    What  effect  on  the  quotient  has  rejecting  equal  factors 
in  both  dividend  and  divisor  ? 

145.  Cancellation  is  the  process  of  shortening  computations 
by  rejecting  or  canceling  equal  factors  from  both  dividend  and 
divisor. 

146.  Example.     Divide  the  product  of  6,  8, 12,  32,  and  84  by 
the  product  of  3,  4,  6,  and  24. 

222       4      28 
X>   *.  *?     i?      =2x2x2. x4x  28=  896. 


SOLUTION.  Do  not  form  the  products,  but  indicate  the  multiplication  by 
the  proper  signs  and  write  the  divisor  below  the  dividend  as  shown  above.  3,  4, 
and  6  in  the  divisor  are  factors  of  6,  8,  and  12,  respectively,  in  the  dividend  ; 
hence,  reject  3,  4,  and  6  in  the  divisor  and  write  2,  2,  and  2,  respectively,  in  the 
dividend  ;  then  cancel  the  common  factor  8  from  24  in  the  divisor  and  32  in  the 
dividend,  retaining  the  factors  3  and  4,  respectively  ;  next  cancel  the  common 
factor  3  in  the  divisor  from  84  in  the  dividend  and  there  remains  the  uncanceled 
factors  2,  2,  2,  4,  and  28  in  the  dividend.  Hence,  the  quotient  is2x2x2x4 
X  28,  or  896. 

WRITTEN  EXERCISE 


l.    14  x  21  x  48  +  7  x  21  x  6  =  ? 


2.  128  x  48  x  88  --  64  x  24  x  4  =  ? 

3.  Divide  128  x  18  x  36  by  64  x  18  x  12. 
12  x  16x24x8  x  92x28^  ? 

6  x  8  x  23  x  7 


110  PRACTICAL   BUSINESS   ARITHMETIC 

5.  If  18  T.  of  hay  cost  $270,  what  will  25  T.  cost  at  the 
same  rate  ? 

6.  How  many  days'  work  at  82.75  will  pay    for  2  A.   of 
land  at  $  110  per  acre? 

7.  If  75  bbl.  of  flour  may  be  made  from  375  bu.  of  wheat, 
how  many  bushek  will  be  required  to  make  120  bbl.  of  flour  ? 

8.  If  45  men  can  complete  a  certain  piece  of  work  in  120 
da.,  how  many  men  can  complete  the  same  piece  of  work  in 
30  da.? 

9.  The  freight  on  350  Ib.  of  evaporated  apricots  is  f  1.47. 
At  that  rate  how  much  freight  should  be  paid  on  7350  Ib.  of 
evaporated  apricots? 

10.  If  15  rm.  of  paper  are  required  to  print  400  copies  of 
a  book  of  300  pp.,  how  many  reams  will  be  required  to  print 
32,000  copies  of  a  book  of  300  pp.  ? 


DIVISORS   AND   MULTIPLES 
COMMON  DIVISORS 

ORAL  EXERCISE 

1.  Name  a  factor  that  is  common  to  35  and  49. 

2.  Name  two  factors  that  are  common  to  both  48  and  64. 

3.  Name  the  greatest  factor  that  is  common  to  75  and  100. 

147.  A  common  divisor  is  a  factor  that  is  common  to  two  or 
more  given  numbers.     The  greatest  common  divisor  (g.  c.  d.)  is 
the  greatest  factor  that  is  common  to  two  or  more  given  numbers. 

148.  Example.     Find  the  g.  c.  d.  of  24,  84,  and  252. 

SOLUTIONS,     (a)  Separate  each  of  the  num- 
bers into  its  prime  factors.    The  factor  2  occurs  (#) 
twice  in  all  .the  numbers  and  the  factor  3  once          24  =2x2x2x3 
in  all  the  numbers.    None  of  the  other  factors          84=2x9x3x7 
occur  in  all  the  numbers;  hence,  2  x  2  x  3,  or 

12,  is  the  greatest  common  divisor  of  24,  84,        *52  =  2x2x3x3x7 
and  252. 


FACTORS,   DIVISORS,   AND   MULTIPLES  111 

(?>)   The  common  prime  factors  of  two  or  more  given  Sl\ 

numbers  may  be  found  by  dividing  the  numbers  by  their  9^04  _  04  _  oco 

prime  factors  successively  until  the  quotients  contain  no  ~ct~~-  - 

common  factor,  as  shown  in  the  margin.  2)L'Z  —  4L  —  12o 

Ever  since  decimal  fractions  came  into  quite  gen-  ^  —  —  ^  —  II  - 

eral  use  the  subject  of  greatest  common  divisor  has  ^  ~~     '  ~~     "1 

been  stripped  of  most  of  its  practical  value.  When  fractions  like  £f  f  ^  were 
quite  generally  used,  it  was  necessary  to  reduce  them  to  their  lowest  terms 
before  they  could  be  conveniently  handled  in  an  operation.  For  this  pur- 
pose, the  greatest  common  divisor  (here  97)  was  found  and  canceled  from 
each  term,  thus  greatly  simplifying  the  fraction  (here  if).  Now,  however, 
the  greatest  common  divisor  of  the  terms  of  the  fractions  used  in  business 
is  easily  found  by  inspection,  and  the  need  for  finding  the  greatest  common 
divisor  is  slight. 

ORAL  EXERCISE 

1.  What  is  the  greatest  common  divisor  of  65  and  75?  of  12 
and  32?  of  75  and  125? 

2.  What  is  the  greatest  common  divisor  of  12,  30,  and  96? 
of  8,  24,  and  42?  of  36,  90,  and  96? 

3.  What  divisor   should    be    used   in    reducing   -^fe   to   its 
lowest  terms?    iff? 


WRITTEN    EXERCISE 

Find  the  greatest  common  divisor  of: 

i.    48,  240.  2.   42,  28,  144.  3.    88,  144,  220. 

4.  A  real  estate  dealer  has  four  plots  of  land  which  he  wishes 
to  divide  into  the  largest  number  of  building  lots  of  the  same 
size.  If  the  plots  contain  168,  280,  182,  and  252  square  rods, 
respectively,  how  many  square  rods  will  there  be  in  each  build- 
ing lot? 

COMMON  MULTIPLES 

ORAL  EXERCISE 

1.  Name  a  multiple  of  7  ;   of  9;    of  16  ;   of  64. 

2.  Name  two  other  multiples  of  each  of  the  above  numbers. 

3.  Name  two  multiples  that  are  common  to  3  and  4  ;   to  5 
and  9;  to  8  and  12.     Which  of  the  multiples  just  named  is  the 
least  common  multiple? 


PRACTICAL   BUSINESS   ARITHMETIC 

149.  A  common  multiple  is  any  integral  number  of  times  two 
or  more  given  numbers.     The  least  common  multiple  (1.  c.  m.) 
of  two  or  more  numbers  is  the  least  number  which  is  an  integral 
number  of  times  e'ach  of  the  given  numbers. 

150.  Example.     Find  the  1.  c.  m.  of  28,  42,  and  84. 

SOLUTIONS.    («)  Resolve  each  of  the  numbers  into  (<*) 

its  prime  factors.     The  factor  2  occurs  twice  in  28  and      90 9  v  9  ./  7 

^O  —   ^J    /\    *^    /\     I 

in  84,  the  factor  3  occurs  once  in  42  and  84,  the  factor  7       4  ~       ~       n       „ 

4    —      x  £j  x  7 
occurs  once  in  each  of  the  numbers.     Therefore,  the 

least  common  multiple  is  2  x  2  x  3  x  7,  or  84  ;  or  84  =2x2xox7 

(6)    Arrange  the  numbers  in  a  horizontal  line  and  divide 
by  any  prime  factor  that   will    exactly  divide  any  two  of  C*) 

them.     Divide  the  numbers  in  the  resulting  quotient  by  any    9)  28      42      84 
prime  factor  that  will  divide  any  two  of  them,  and  so  con-    o  \  -11 9! To 

tinue  the  operation  until  quotients  are  found  that  are  prime       ^ — — — 

to  each  other.     Find  the  product  of  the  several  divisors  and       *•')  *       ^*- 

the  last  quotients  and  the  result  is  the  I.e. in.     2x2x3x7       7)  7         7         7 

=  84,  the  1.  c.  m.  ~J        J         J 

All  numbers  that  are  factors  of  other  given  numbers  may 
be   disregarded  in  finding  the  1.  c.  m.       Thus  the   common   multiples  of  4,  8, 
16,  32,  64,  and  80  are  the  same  as  the  multiples  of  04  and  80. 


ORAL  EXERCISE 

State  the  least  common  multiple  of: 

1.  6,  5,  and  3.  4.  2,  4,  7,  8,  48,  24.  . 

2.  6,  8,  12,  and  24.  5.  G,  42,  84,  1(38,  336. 

3.  4,  5,  15,  and  30.  6.  5,  15,  75,  150,  300. 

WRITTEN   EXERCISE 

Find  the  least  common  multiple  of: 

1.  6,  7,  8,  and  5.  5.  4,  20,  12,  and  48. 

2.  6,  18,  24,  and  84.  6.  62,  78,  30,  and  142. 

3.  12,  24,  36,  and  96.  7.  35,  105,  125,  and  225. 

4.  32,  46,  92,  and  128.                       8.  114,  240,  72,  and  320. 
9.    What   number  is  that   of  which  2,  3,  5,  and  11  are  the 

only  prime  factors? 


CHAPTER   XII 

COMMON  FRACTIONS 
ORAL  EXERCISE 

1.  When  a  quantity  is  divided  into  3  equal  parts,  what  is 
each  part    called?  into  8  equal  parts?  into  12  equal  parts? 

2.  The  shaded  part  of  A  is  what  part  of  the  whole  hexagon  ? 
the  shaded  part  of  B  ?  the  shaded  part 

of  C? 

3.  In  the   shaded   part  of   A  how 
many  sixths  ?  in  the  shaded  part  of  B  ? 

4.  One  half    of   the    hexagon    is    how   many   sixths    of   it  ? 
How  many  sixths  in  the  whole  hexagon? 

5.  In  the  unshaded  part  of  B  how  many  thirds?    Two  thirds 
are  how  many  sixths? 

6.  In  the  unshaded  part  of  C  how  many  sixths? 

7.  Read  the  following  fractions  in  the  order  of  their   size, 
the  largest  first :   i,  f ,  f ,  J,  J,  |,   J. 

8.  Complete  the  following  statement :    Such  parts  of  a  unit 
as  .5,  .25,  ^,  |,  etc.,  are  called  . 

151.  Common  fractions  are  expressed  by  two  numbers,  one 
written  above  and  one  below  a  short  horizontal  line. 

152.  The    number  written    above    the    line    is    called    the 
numerator    of    the    fraction,  and    the    number  written    below, 
the  denominator  of  the  fraction. 

153.  The  numerator  tells  the  number  of  parts  expressed  by 
the  fraction ;   the  denominator   names   the  parts    expressed   by 
the  fraction. 

Thus,'  in  the  fraction  f ,  4  tells  that  a  number  has   been  divided   into 
four  equal  parts  and  3  shows  that  three  of  these  parts  have  been  taken. 

113 


114  PRACTICAL   BUSINESS   ARITHMETIC 

154.  It  is  clear  that  the  greater  the  number  of  equal  parts 
into  which  a  unit  is    divided,  the    less    is    the    value    of    each 
part ;  and  the  less  the  number    of    equal    parts    into  which    a 
unit  is  divided,  the  greater  the  value    of    each    part.       Hence, 

Of  two  fractions  having  the  same  denominator,  the  one  having 
the  greater  numerator  expresses  the  greater  value;  and 

Of  two  fractions  having  the  sime  numerator,  the  one  having  the 
smaller  denominator  expresses  the  greater  value. 

155.  The  terms  of  a  fraction  are  the  numerator  and  denomi- 
nator taken  together. 

156.  A  unit  fraction  is  a  fraction  whose  numerator  is  one. 
Thus  $,  |,  £,  and  Jg  are  unit  fractions.     J  in.  is  read  one  third  of  an  inch. 

157.  An  improper  fraction    is    a    fraction  whose   numerator 
is  equal  to  or  greater  than  its  denominator. 

Thus,  f,  f,  and  235-  are  improper  fractions.  The  value  of  an  improper 
fraction  is  always  equal  to  or  greater  than  one. 

158.  A  mixed  number  is  the  sum. of  a   whole  number  and 
a  fraction. 

Thus,  2}  and  4f,  read  two  and  one  seventh  and  four  and  two  ffths,  are 
mixed  numbers. 

ORAL  EXERCISE 

1.  What  takes  the  place  of  the  denominator  in  .5?  in  .25? 

2.  Read  aloud  the  following  fractions  in  the  order  of  their 
size,  the  largest  first :  J,  ^  J,  J,  J,  ^,  J,  |,  ^,  fa,  TJT. 

3.  Read  aloud  the  following  fractions  in  the  order  of  their 
size,  the  smallest  first:  f,  f,  J,  f,  1,  f,  ^  J,  f,  f,  ^,  f 

4.  Read  aloud  the  following:   |   mi.;   |T. ;   27|  yd.;    yy^-g- 
cu.  ft.;   275|  A.;   250 &  lb.;   £  18&  ;   X  271 J  ;  TJ¥  sq.  ft. 

5.  Of  the  total  cotton  produced  in  the  United  States  in  a 
recent  year    the   principal    cotton-growing   states    contributed 
approximately  as  follows  :    North  Carolina,  ^  ;   South    Caro- 
lina, -j1^  ;   Georgia,  i  ;   Florida,  T^Q  ;  Alabama,  ^  ;   Mississippi, 
Y  ;   Louisiana,   -^  ;    Texas,  ^  ;    Arkansas,    ^  ;    Tennessee,  -g1^. 
Name  the  principal  cotton-growing  states,  in  the  order  .of  pro- 
duction, for  this  year. 


COMMON   FRACTIONS  115 

REDUCTION 
To  HIGHER  TERMS 

ORAL  EXERCISE 

1.  How  many  halves  in  1?  how  many  fourths?  how  many 
eighths?  how  many  sixteenths? 

2.  How    many    fourths    in    J? 
how   many    eighths?    how   many 
sixteenths  ? 

3.  How  many  eighths  in  |  ?  how  many  sixteenths  ? 

4.  How  many  fourths  in  -£|  ?  how  many  eighths  in  1 J  ?  how 
many  halves  in  T8g  ? 

5.  What  effect  is  produced  upon  the  value  of  a  fraction  by 
multiplying  or  dividing  both  terms  of  a  fraction  by  the  same 
number  ? 

6.  Change  14  gal.  to  quarts.     Compare  the  size  of  the  units 
in  14  gal.  with  the  size  of  the  units  in  56  qt.  ;  the  number  of 
units  ;  the  value  of  the  two  numbers. 

7.  Change  i  to  twelfths  ;   J;   |;   J  ;   f ;   |;   |. 

8.  Name  three  fractions  equal  in  value  to  £ ;  to  f ;  to  |. 

159.  It  has  been  seen  that  multiplying  or  dividing  both  terms 
of  a  fraction  by  the  same  number  does  not  change  the  value  of  the 
fraction. 

160.  A  fraction  is  reduced  to  higher  terms  when  the  given 
numerator  and  denominator  are  expressed  in  larger  numbers. 

ORAL   EXERCISE 

1.  Reduce  to  twelfths  :  1,  f ,  f . 

2.  Reduce  to  sixteenths  :   |,  |,  | ,  $-. 

3.  Reduce  to  twentieths:  -|,  |,  y3^,  -|,  -|. 

4.  Reduce  to  twenty-fourths :   |,  f ,  |,  ^  j,  J- 

5.  Reduce  to  thirty-seconds:  J,  f,  f,  f,  fV  yg-i  ^  yV 

6.  Reduce  to  one-hundredths  :  |,  J,  -|,  y^,  ^*§>  2lr  ?'  2~s* 

7.  Reduce  |  and  f  to  fractions  having  the  denominator  24. 


116  PRACTICAL   BUSINESS   ARITHMETIC 


To  LOWEST  TERMS 

ORAL   EXERCISE 

1.  28f  equals  how  many  thirds?  J|  equals  how  many  halves? 

2.  Name  the  largest  possible  unit  frac-     _ 
tion.     Why  is  this  the  largest  possible 
unit  fraction  ? 

3.  Change  -f%  to  the  largest  possible 


unit  fraction  ;  ^  ;  T2^  ;  ffa  ;  J^.     Express  1  J  in  its  simplest 
form.     Reduce    2      to  ^ts  lowest  terms. 


161.  A  fraction    is  reduced  to  its   lowest   terms  when   the 
numerator  and  denominator  are  changed  to  numbers  that  are 
mutually  prime. 

162.  Example.    Reduce  -ffy  to  its  lowest  terms. 

SOLUTION.     6  is  a  common  factor  of  96  and  108  ;  dividing 

both  terms  by  6,  the  result  is  {f.     2  is  a  common  factor  of        _£JL  =  1&  —  1 
16  and  18  ;  dividing  both  terms  by  2,  the  result  is  f . 

ORAL  EXERCISE 

1.  Reduce  to  fifteenths:  1,  f,  f,  f. 

2.  Reduce  to  eighths :   ^  |,  f ,  if,  l|,  \. 

3.  Reduce  to  fiftieths:   J,  jj,  ^fr,  ^,  &,  2^0- 

4.  Change  to  twentieths :   |>  T7^,  £,  f ,  |,  -^,  |. 

5.  Reduce  to  lowest  terms :   ^g,  T8^,  T82,  f|,  ^  f , 


WRITTEN  EXERCISE 

1.  Reduce  to  sixteenths  :   \^  l|§,  |,  |f,  f,  lf£. 

2.  Reduce  to  lowest  terms:   fT22\  cu.   ft.,  ^   A.,   ^Vo   T- 

3.  Reduce  to  lowest  terms :   Jjffl  mi.,  £JJ^,  |f||  lb.,  |f  mi. 

4.  Reduce  to  three-hundred-twentieths:   |  mi.,  |  mi.,  Jg-   mi- 

5.  Reduce  to  their  simplest  common  fractional  form  :  |f  f  $  T., 
U  T,  T%  A,  lfj  A.,  ||§  sq.  mi.,  llf  8q.  mi.,  ||f  mi. 


COMMON    FRACTIONS  117 


INTEGERS  AND  MIXED  NUMBERS  TO  IMPROPER  FRACTIONS 

ORAL  EXERCISE 

1.  How  many  quarts  in  1  gal.?     in  3  gal.? 

2.  How  many  sixths  in  1?     in  3?     in  5?     in  7? 

3.  How  many  fifths  in  1?     in  1J?     in  If?     in  3J? 

4.  Express  as  fourths :  61,  12|,  13,  87,  6lj,  28J. 

5.  Express  as  eighths:   15,  12,  10  j,  1J,   2f,  If,  9|. 

6.  Express  as  halves:   27,  14,301,  1711,  1821,  249. 

WRITTEN  EXERCISE 

Reduce  to  improper  fractions : 

1.  831.  4.    666|.  7.    265^.  10.    3150J. 

2.  166|.     5.  ISO^.     8.  319T5g.     11.  1625J. 

3.  3331.     6.  212^.     9.  146l|.     12.  2: 


IMPROPER  FRACTIONS  TO  INTEGERS  OR  MIXED  NUMBERS 


ORAL   EXERCISE 

1.  How  many  quarters  of  a  dollar  in  $25?     iff-  =  ? 

2.  Change  to  integers  :  If  a,  -ija,  l^2-,   \8/-,  i|J^,  l||o. 

3.  Express  28  J  as  fourths  ;  express  -^J3-  as  a  mixed  number. 

4.  Change    to    mixed   numbers:      ^-,    ^p,    if1,    ^f1,    ^. 

5.  What  is  the  value  of:  -2T^8-  lb.?  l*£  lb.?  l|A  bu.?  ^  pk.? 

ft-?  -4w°-  A-?  Hi  mi-?  -¥2°-  lb-?  ill  S(l-  ft-? 


WRITTEN   EXERCISE 

Reduce  to  integers  or  mixed  numbers: 

1.  §13  mi.  4.    -Vg^A.  7.    4$*  lb. 

2.  -V&4A.  5.    l|i|T.  8.    ffflou.  ft. 

3.  |i||T.  6.    IfffT.  9.    J^sq.mi. 
163.    Wlien  expressing  final  results  reduce  all  proper  frac- 

tions  to   their   lowest    terms    and    all    improper    fractions   to 
integers  or  mixed  numbers. 


118  PRACTICAL   BUSINESS   ARITHMETIC 

To  LEAST  COMMON  DENOMINATOR 

ORAL  EXERCISE 

1.  How  many  pounds  in  1  T.  500  Ib.  ?  5  T.  +  1000  Ib.  =  ?  Ib. 
5  T.  1000  Ib.  =  ?*T. 

2.  How   must   numbers  be  expressed    before   they    can   be 
added  or  subtracted? 

4.  What  kind  of  fractions  can  be  added  or  subtracted? 

5.  Express  |  as  sixteenths.     Add  |  and  -f^  ;   J  and  ^  ;   f 
and  J. 

o 

6.  Express  J  as  eighths.     Subtract  J  and  |  ;   1  and  T3g  ;   | 
and  Jg. 

164.  Two  or  more  fractions  whose  denominators  are  the  same 
are  said  to  have  a  common  denominator;  if  this  denominator 
is  the  smallest  possible,  the  fractions  are  said  to  have  a  least 
common  denominator.  Two  or  more  fractions  having  the  same 
denominator  are  sometimes  called  similar  fractions. 

ORAL  EXERCISE 

Change  to  similar  fractions : 

1.  J,  f  6.    f  1.  11.  f,  J.  16.  J,  |,  1. 

2.  J,l.  7.     f,  |.  12.  1,  /g.  17.  1,   1,  |. 

3.  1    f  8.    1,  f .  13.  |,  ^_  18-  i  i>  A- 

4.  |,  1.  9.    |,  §.  14.  j,  TV  19.  1,  |,  |. 

5'     !'   140'  10'    i  f  15'     8'   1T0-  20-     2'  I'  T6- 

WRITTEN  EXERCISE 
Change  to  fractions  having  the  least  common  denominator  : 

T       JL    _^5 .     i8  ^5j^57  ol521 

8'   32'   64"  (P    81  12'  112'  12'  ^'   3^'   48* 

5'  17'  2^5^*  ^'  "5'   36'   45*  56'   32'  It'   6^' 

<a       1      1      1     1  irlT         917  11          153175 

J'     ¥'   2'    §'  ^'  7<     1'  16'   32'  64'  "'  F20'   4'  160'   8* 

4      ^    -7-    —3—    2.  o      _9_     _5      _7_    1  no  -LQ-    _6_    J—    -5- 

Change  the  fractions  to  form  for  addition  or  subtraction: 

13.    81ft,  7ft.         14.    184ft,  112ft.         15.    6126ft,  178ft. 


COMMON   FRACTIONS  119 

ADDITION 

165.    It  has  been  seen  that  only  like  numbers  and  parts  of 
like  units  can  be  added. 

ORAL  EXERCISE 
State  the  sum  of: 

1.  },  |,  f.  7.    21,  8j,  12},  19}. 

2.  |,  f,  \.  8.   5J,  12},  7},  10}. 

3.  },  |,  f  9.    7|,  2|,  8},  H,  2i. 

«•     I2!'   A-    iV  10'     23>   6I'   %    12i   10f- 

5-  },  i  f,  f  f  11.    1},  10|,  16},  18},  121. 

6-  7  '         I2- 


Ity  horizontal  addition  find  the  sum  of: 

13.  2  pieces  of  gingham  containing  411  and  432  yd. 

In  the  dry-goods  business  fourths  (quarters)  are  very  common  fractions. 
They  are  usually  written  without  denominators  by  placing  the  numerators 
a  little  above  the  integers.  Thus,  5  11  equals  51£,  542  equals  54|  (54|),  and 
523  equals  52|. 

14.  4  pc.  stripe  containing  421,  381,  4C2,  and  49  yd. 

15.  3  pc.  fancy  plaid  containing  421,  402,  and  41  yd. 

16.  4  pc.  duck  containing  481,  473,  462,  and  402  yd. 

17.  2  pc.  monument  cotton  containing  542  and  552  yd. 

18.  4  pc.  dress  silk  containing  321,  342,  353,  and  322  yd. 

166.    Examples,     l.    Find  the  sum  of  J-  and  |. 

SOLUTION.  |  and  f  are  not  similar  fractions  ;  1.  c.  m.  of  8  and  5  =  40 
hence,  make  them  similar  by  reducing  them  to  7  _  35..  2  _  16 

equivalent  fractions  having  a  least  common  de-  86       1«       51      111 

nominator.      |  =  f  s  and  |  =  i«-.      f  jj  +  $%  =  |i  47  +  47  =  4  0  =  ^  10" 

=  1H- 

2.    Find  the  sum  of  56J,  34J,  52|. 

SOLUTION.    By  inspection  determine  the  least  common  56—    =    8 

denominator  of  the  given  fractions  ;  then  make  the  frac-  ^41.    _     ^ 

tions  similar  and  add  them,  as  shown   in   the   margin.  __^          . 

The  result  is  lj\,  which  added  to  the  sum  of  the  inte-  ^ 
gers  equals  1432\,  the  required  result. 


120  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN   EXERCISE 

Find  the  sum  of: 

i.    TV  f.  7.    12  f,  172-.V 

2.  £,jf  8-  8iii 

3.  2i,17i.  9.  52|,  59|,  57 

4.  12},  19^-  10.  60f,  18},  21£,  142TV 

5.  l,4i,19i.  11.  20i,  121,  181,  921,  75f 

6.  21,  4f,'25T9g.  12.  140|,  260J,  145|,  216 J,  3901. 

13.  A  carpet  dealer  sold  at  different  times  125|  yd.,  272^ 
yd.,  1691  yd.,  186|    yd.,  241|  yd.,  265|   yd.,  296J   yd.,  and 
314|  yd.  of  Axrainster  carpet,  at  $>2.65  per  yard.     If  it  cost 
him  $2.45  per  yard,  what  was  his -gain? 

14.  A  dry-goods  merchant  bought  50  pc.   of    dress  silk  at 
81  per  yard.     If  the  pieces  contained  421,  432,  442,  473,  441,  452, 
403,  462,  45i,  42,  47i,  482,  403,  401,  402,  403,  502,  403,  472,  483,  403, 
451,  402,  452,  442,  473,  462,  411,  513,  423,  532,  572,  531,  511,  483,  472, 
401,  452,  452,  403,  401,  453,  472,  481,  511,  522,  572,  613,  602,  50i  yd., 
respectively,  and  he  sold  the  entire  purchase  at  $1.25  per  yard, 
what  was  his  gain? 

SHORT  METHODS  IN  ADDITION 

ORAL  EXERCISE 

1.  i  -|-  1  =  1&      Observe   that  the  numerator  of  the  sum  is 

/         y        \>  o 

equal  to  the  sum  of  the  denominators  in  the  given  fractions. 

2.  -1  +  1  =  ?     Give  a  short  method  for  adding  any  two  sim- 
ple fractions  whose  numerators  are  1. 

3.  |  -j-  |  =  ^.     Observe  that  the  numerator  of  the  sum  is 
equal  to  the  sum  of  the  denominators  multiplied  by  the  numera- 
tor of  either  of  the  given  fractions. 

4.  |  +  !=  ?     Give  a  short  method  for  adding  any  two  frac- 
tions whose  numerators  are  alike. 

5.  Find  the  sum  of  J,  |,  and  1- 

SOLUTION.     ^  -f  £  =  T7Z  ;  T72  +  3  =  |^,  the  required  result. 


COMMON   FRACTIONS  121 

ORAL  EXERCISE 

State  the  sum  of: 

1.  -|,  J.  7.  |,  J.  13.  \,  1.  19.  |,  $. 

2.  1,1-  8.  i    1,  14.  |,f  20.  f,TV 

3.  A    i.  9.  if  15.  f,  f.  21.  1,1,1 

4.  A,  f  10.  f,|.  16.  |,f.  22.  |,11. 

5.  i    f  11.  |,  f .  17.  |,  |,  23.  1    f  f 

6.  -l,f  12.  |,  f.  18.  f,  |.  24.  f,  |,|. 

167.  The  most  common  business  fractions  are  usually  small 
and  of  such  a  nature  that  they  may  be  added  with  equally  as 
much  ease  as  integers.     The  following  exercise  will  be  found 
helpful  to  the  student   in   learning  to   add   these   fractions   in 
practically  the  same  manner  that  he  adds  integers. 

168.  Example.    Find  the  sum  of  T5g,  |,  f ,  and  J. 

SOLUTION.  By  inspection  determine  that  the  least  common  denominator  is 
16.  Then  mentally  reduce  each  fraction  to  IGths  and  add  as  in  whole  numbers. 
Thus,  5,  7,  19,  f|,  lii. 

ORAL  EXERCISE 
Find  the  sum  of: 
1.  2.  3.  4.  5.  6.  7.  8.  9.          10. 

iiii  i          2.          i          a          i 

3342463^49 

11.  12.          13.          14.          15.          16.          17.          18.         19.         20. 

1421171141 
3  ~5"~3"1F~8~'5~'3"'3~~5"2 

3.  3.  5  3  1  1  3.  1  1  1 

5  5  6  Y  6  3  4  5  2  5 

t    .  i      I.     f :-  .  r    .  i    ,4     .*..    .  it .  :  i 

i       i      4       4      t      i     -i      4      i      i 

2  .7^  3  3  1  314.3.3. 

3  "10  Y  ¥  855 

4      A     A      *       I       f       I      I -4      A 

i       i%      A       f       i       A       i       4       4      A 
-I       A      A       i       e5       41-     A      4       i      A 


122  PRACTICAL   BUSINESS   ARITHMETIC 

Exercises  similar  to  the  foregoing  should  be  continued  until  the  student 
can  name  the  successive  results  in  the  addition  without  hesitation. 

169.  The  ordinary  mixed  numbers  that  come  to  an  accountant 
should  be  arranged  for   addition  practically  the   same  as  in- 
tegers.    In  adding,  the  fractions  should  be  combined  first  and 
then  the  integers. 

170.  Example.    Find  the  sum  of  2J,  5^,  and  3|. 

W2~ 
SOLUTION.   By  inspection  determine  that  the  least  common  denomi-       c  i 

nator  of  the  fractions  is  8.     Mentally  find  the  sum  of  the  fractions  and         * 
the  result  is  If.    Add  this  result  to  the  integers  and  the  entire  sum  is  11|.          8 


ORAL   EXERCISE 

State  the  sum  of  : 

1.            2.          3.          4.          5.          6.           7.  8.  9.  10. 

2J       31      3J      81      14i       5f       41  2J  3|  14-1 

H       2£5J_7J.17fl8JH16|17J.  ^i 

11.        12.            13.          14.         15.        16.         17.         18.  19.  20. 

9f       5f       11        If      8J       4|       51  41  41  4|- 

41        2|        6J       3|       21      2f       5|  2f  .    If 

l        7&       5-J       2Tij      41       41        6|  6£  '7f 

4^      3|       6J        21  8^ 


21.  22.  23.  24.  25.  26.  27.  28.  29.  30. 

£  1  £2  92  13  £53  91  11  11  91  £M 

¥  o  a  7"  I  S"              6^  Q  ^  ^5~ 

31  11  1J  ?|  s|  3J-  7f  2J  9f  4 

4i  !J  2f  2f  51  3J  3|  7|  41  21 


Exercises  similar  to  the  above  should  be  continued  until  the  student  can 
add  with  great  facility.  If  the  principles  of  grouping  have  not  been  well 
mastered,  simple  addition  should  be  carefully  reviewed. 


COMMON   FRACTIONS 


123 


WRITTEN  EXERCISE 

or  write  from  dictation  and  find  the  sum  of: 

3.         4.         5. 


Copy 

or  write,  fr 

1. 

2. 

1649J 

1672f 

43721 

1485| 

8431| 

16351 

51321 

12641 

16541 

1269f 

1831f 

17481 

1831| 

1936| 

14621 

54131 

18511 

2114ft 

1114ft 

1116ft 

7. 

8. 

91241 

7249J 

2716J 

2724| 

25141 

86921 

29671 

24761 

2964^ 

86951 

68751 

62141 

8875f 

72411 

26581 

86141 

8425| 

4725^ 

8273| 

1649^ 

1782f 

12861 

86951 

62481 

24721 

1286-1 

62731 

8537f 

9685f 

6982^ 

96851J 

3685-1 

1925-/2 

2614f 

4212ft 

87961 

2729TL 

1592| 

14361 

1390f 

24151 

18671 

16391 

4136| 

16521 

31161 

1439TV 

2243ft 

9. 

16491 
27241 
86951 
15651 
27241 
86191 
2924f 
65291 
85921 
27251 
8647| 
8725f 
62191 
84131 
7226f 
18251 
47251 
2816f 
25191 


21101 
16401 
36801 
45901 
2169f 
8432| 
40411 
6542f 
1862§ 
3246 1 


10. 

75291 
62141 


62141 
1745J 
3146f 
1864-1 

28391 


4036| 

8130ft 

2148ft 


6. 

12141 
2167^ 
31591 
92751 
7215f 
52611 
7215| 
5144f 
6257| 


8614f 
9215f 
6719f 
8516^ 
7528J 
7216f 
67291 
35141 
1686f 
1725J 
2538f 
1758| 
2752-1 
21141 
22161 
18721 


11. 

73651 
26141 
15831 
16951 
17621 
1875| 
16291 
7214| 
2510-1 
2625f 
86141 
27291 
28161 
28141 
2716| 
17621 
18751 
26141 


12. 


28141 
2910J 


27141 
2913J 
2874f 
2619f 
1472^ 


1813^ 
19621 
18621 
17591 
2864| 
1624J 
17291 
1805| 


1465f 


124 


PRACTICAL   BUSINESS   ARITHMETIC 


SUBTRACTION 

ORAL  EXERCISE 

1.  172  A. -154  A.  =  ?     f-j  =  ?     Ibu. -3pk.  =  ? 

2.  Find  the  difference  between  |  and  j-  ;  J  and  ^;   J  and  ^; 
f  and  f . 

171.  It  is  clear  that  only  like  numbers  and  parts  of  like  units 
can  be  subtracted. 

172.  Examples,     l.    Find  the  difference  between  J  and  T5^. 
SOLUTION.     The  given  fractions  must  be  reduced  to  equivalent  fractions  having 

a  least  common  denominator.  The  least  common  denominator  is  24.  £  =  f  £  and 
fa  —  M-  li  —  H  =  ii»  tne  required  result. 

2.    From  211  take  17J-. 

SOLUTION.  Change  the  given  fractions  to  similar  fractions  as  in  example  1. 
f  cannot  be  subtracted  from  §,  hence  1  is  taken  from  21  and  mentally  united 
to  f ,  making  f .  f  from  |  leaves  f ,  and  17  from  20  leaves  3.  The  required  result 
is  therefore  3|. 


Find  the  value  of: 


2. 
3- 

*• 


-If 


ORAL   EXERCISE 
5.     4|-lf. 

8.    I2J-6J. 


9.  5U- 

10.  45-16-f. 

11.  11|— 6f. 

12.  70|  - 


The  following  is  a  recent  clipping  from  a  daily  paper.  It  shows  the 
prices  of  wheat  on  the  Chicago  market.  The  first  line  of  prices  is  for  wheat 
to  be  delivered  in  July,  and  the  second  line  for  wheat  to  be  delivered  in 
September. 

CHICAGO  WHEAT  QUOTATIONS 


DELIVERY 


PREVIOUS  CLOSING 


Ol'KMNG 


HIGHEST 


LOWEST 


CLOSING 


July 
September 


87^ 


87^ 


13.-  What  was  the  difference  between  the  highest  and  the 
lowest  price  of  July  wheat  ?  of  September  wheat  ? 

14.  What  wras  the  difference  between  the  opening  and  the 
closing  price  of  September  wheat  ?  of  July  wheat  ? 


COMMON   FRACTIONS  125 

15.  What  was  the  difference  between  the  opening  price  and 
the  previous  closing  (yesterday's  closing)  price  of  July  wheat  ? 
of  September  wheat  ? 

16.  A  bought  1000  bu.  July  wheat  at  the  lowest  price  and 
sold  the  same  at  the  closing  price.     What  was  his  gain  ? 

SUGGESTION.     1 J  ^  =  $0.015 ;  1000  times  f  0.015  =  $  ? 

17.  B  bought   1000    bu.    September  wheat  at   the  opening 
price  and  sold  it  at  the  highest  price.     What  was  his  gain? 
Had  he  bought  at  the  lowest  price  and  sold  at  the  closing  price, 
what  would  have  been  his  gain  ? 

18.  C  bought  25,000  bu.  July  wheat  at  the  opening  price  and 
sold  it  at  the  highest  price.     What  was  his  gain  ? 

WRITTEN   EXERCISE 
Find  the  value  of: 

1.  39-115  5.    1651  -41^V.  9.   l-i-i 

O  3  o  4)  o  4  o 

2.  85-21f.  6.    2451-17-!%.  10.   J  -  T96-  -  f . 

3.  168 -45f.  7.   177f-17TV  11.    2J+lf-L&. 

4.  26lT9g-131l.         8.   2150-121-if.          12.    251  -  8|  -  151. 

173.  When  the  numerators  of  any  two  fractions  are  alike,  the 
subtraction  may  be  performed  as  in  the  following  examples. 

174.  Examples,     l.    From  i  take  4.     2.    From  4  take  f . 

jr  i  y  o  o 

SOLUTIONS.  1.  9  —  7  =  2,  the  new  numerator.  0  x  7  =  63,  the  new  denomi- 
nator. Therefore,  the  required  result  is  ^.  2.  8  —  5x3  =  9,  the  new  numer- 
ator. 8  x  5  =  40,  the  new  denominator.  Therefore,  ^  is  the  required  result. 

ORAL  EXERCISE 

State  the  value  of: 
1.    1  -  1.  8.    |-  -  |.  15.    i  -  J.  22.    |  -  f . 

2-  i-i-  9-  i-i-  16.  1-1-  23.  |-f 

3.  1-1.  10.  \-\.  17.  f-f.  24.  f-f. 

4.  1-f  11.  i-1.  18.  f-f.  25.  12J-6&. 

5.  J-l.  12.  |-f  19.  |-f  26.  131-21. 

6.  1-1.  13.  1-|.  20.  |-f.  27.  l-H-71. 

7.  i-f  14.  1-f  21.  f-f.  28.  16f-12|. 


126  PRACTICAL   BUSINESS   ARITHMETIC 

MULTIPLICATION 

ORAL  EXERCISE 

1.  12  times  2  A.  are  how  many  acres?     12  times  2  fifths  (f) 
are  how  many  fifths  ?     -^  =  ? 

2.  32  mi.  divided  by  4  equals  how  many  miles?     |  of  32  mi. 
equals  how  many  miles?     Multiplying  by  |,  J,  J,  and  i,  etc.,  is 
the  same  as  dividing  by  what  integer  ? 

3.  If  5  men  can  dig  125  bu.  of  potatoes  in  1  da.,  how  many 
bushels  can  3  men  dig  in  the  same  time  ?     |  of  125  bu.  equals 
how  many  bushels  ? 

175.  Example.     Multiply  f  by  248. 

00 

SOLUTIONS,    (a)  248  times  3  eighths  =  744  eighths       |  X  248  =  ^|-=  93 
=  ^=93;  but,  (J) 

(&)  If  the  multiplication  is  indicated  as  in   the 
margin,  the  work  may  be  shortened  by  cancellation.  £7!$  times  3  __  gg 

P 

176.  Therefore,  to  find   the   product   of   an   integer   and  a 
fraction,  find  the  product  of  the  integer  and  the  numerator,  and 
divide  it  by  the  denominator. 

Before  actually  multiplying,  indicate   the  multiplication  and  cancel  if 
possible. 

ORAL  EXERCISE 


1.  If  1  yd.  of  cloth  costs   I0.87J  (|J),    what  will   16  yd. 
cost?    48  yd.?  128  yd.?  72  yd.? 

2.  When  oats  cost  $0.  33^  ($l)  a  bushel,  how  much  must 
be  paid  for  29  bu.?  for  36  bu.?  for  129  bu.  ? 

3.  A  boy  earns  $0.75  (-If)  a  day.     How  much  will  he  earn 
in  18  da.?  in  40  da.?  in  84  da.?  in  128  da.?  in  160  da.? 

4.  When  property  rents  for  8720  a  year,  what  is  the  rent 
for  1  yr.?  for  \  yr.?  for  1  yr.?  for  -^  yr.  ?  for  1  yr.? 

5.  A   ship    is   worth   848,000.       What    is    \   of   the   ship 
worth  ?  -Jg  of  the  ship  ?  f  of  the  ship  ?  -J  of  the  ship  ?  ^  of 
the  ship  ? 


COMMON   FRACTIONS 


127 


WRITTEN    EXERCISE 


Find  the  product  of: 
1.    98  x  |.  7.    |  of  95. 

8.  fof25. 

9.  f  of  88. 


2.  80  xf. 

3.  50  X  27¥. 

4.  97  x  TV 

5.  92  X  i5^. 

6.  188  x  ^ 


13.  784  x  f 

14.  459xf 
is.  400  x  Jg 

10.    T9g  of  51.      16.  510  x  T7o 


11.    ^¥of99. 


17.    990  x  eV 


19.  f  of  2420. 

20.  |  of  2500. 

21.  |  of  3240. 

22.  f  of  5117. 

23.  J   of  7254. 


12.    ^  of  77.      18.    800  x  if.      24. 


177.    Example.     Multiply  25  by  4|. 


25 


SOLUTION.      |  of  25  =  \5-  or  9|.     Write  f   as  shown  in  the  margin, 
and  carry  9  to  the  product  of  the  integers.     4  x  25  +  9  =  109.     There-          ^"8 
fore,  25  multiplied  by  4f  =  109 1.  109| 

178.  Therefore,  to  find  the  product  of  a  mixed  number 
and  a  whole  number,  multiply  the  integer  and  the  fraction  sepa- 
rately and  find  the  sum  of  the  products. 


ORAL 

Find  the  cost  of: 

1.  15f  Ib.  of  fish  at  9  £ 

2.  7|  yd.  of  cloth  at  13. 

3.  16  Ib.  of  beef  at  10  *  £ 

4.  16J  Ib.  of  sugar  at  5^. 

5.  12 Vd.  of  cloth  at  11  j£ 


EXERCISE 

6.  6|  bu.  turnips  at 

7.  12-i-  bu.  of  oats  at 

8.  10-J  yd.  of  calico  at 

9.  16J  yd.  of  ribbon  at 

10.    8J  gal.  of  molasses  at  25^. 


WRITTEN    EXERCISE 


1.  Find  the  total  cost  of : 
124  Ib.  beef  at  9j£ 

112 1  Ib.  beef  at  5£ 
136  Ib.  pork  at  5^. 

2.  Find  the  total  cost  of  : 
273  yd.  crepe  at  1 2. 
282yd.  satin  at  1 2. 
253yd.  dress  silk  at  1 2.50. 
181  yd.  velvet  ribbon  at  f  2. 


114f  Ib.  fish  at  If. 
156  Ib.  pork  at  l^t. 
131T7g  Ib.  fish  at  9£ 

123  yd.  fancy  stripe  at  $0.50. 
432  yd.  English  serge  at  11.75. 
432  yd.  English  camel's  hair  at  f  2. 
8  pc.  fancy  black  ribbon  at  f  2. 87J. 


128 


PRACTICAL   BUSINESS   ARITHMETIC 


3.  A  merchant  bought  25  pc.  of  striped  denim  containing  411, 
411,  422,  432,  421,  442,  431,  402,  421,  453,  421,  402,  412,  473,  451, 
411,  432,  472,  443,  423,  432^  391^  42i,  432,  and  47  yd.,  at  11^  per 
yard.       If  he  sold  the  first  11  pc.   at  15^  per  yard  and  the 
remainder  at  17^  per  yard,   what  was  his  gain? 

4.  Copy  and  find  the  amount  of  the  following  bill: 


Terttis 


Bought  of 


Eureka  Mills 


^c 


<z^g?^?^ 


;TZ^/''2^-_. 


/  0 


-^Z2-4>- 


179.  The  expressions  ^  of  |  and  \  x  |  have  the  same  meaning  ; 
hence,  the  sign  of  multiplication  may  be  read  0/j  or  multiplied 
by,  when  it  immediately  follows  a  fraction. 

180.  Examples.     1.    Multiply  f  by  f . 

SOLUTION.     To  multiply  f  by  f  is  to  find  f  of  f . 

Let  the  line  AF  in  the  accompanying  diagram  represent  a  unit  divided  into 
5  equal  parts. 

Then  AD  will  represent  f.     Sub-     A 
divide  each   of   the  five  equal  parts 


into  3  equal  parts  and  the  line  AF 
will  represent  a  unit  divided  into  15 
equal  parts,  each  of  which  is  ^  of  the  whole.  It  is  then  clear  that  |  of  $ 
equals  ^5.  Since  1  of  £  is  T^,  |  of  f  is  T\.  But  f  of  f  is  2  times  |  of  f  ;  there- 
fore, §  of  |  equals  r%. 

2.    Find  the  product  of  2|,  |,  and  T7^. 

SOLUTION.      Reduce  the    mixed   number  2£  to   an   im-  ^ 

proper  fraction  and  obtain  |.     Cancel,  and  there  remains  in  „       .        „        ^. 

the  numerators  2  times  7,  and  in  the  denominators  15,  from  ^  X  —  X  —  =  — 

which  obtain  the  fraction      .  JS      £      15      15 


COMMON  FRACTIONS 


129 


181.    Hence,  to  multiply  a  fraction  by  a  fraction  : 

Reduce  the  mixed  numbers  and  integers  to  improper  fractions 

and  cancel  all  factors  common  to  the  numerators  and  denominators. 
Find  the  product  of  the  remaining  numerators  for  the  required 

numerator,  and  the  product  of  the  remaining  denominators  for  the 

required  denominator. 

ORAL  EXERCISE 

1.  How  many  yards  hi  §  rd.  ?    feet  in  f  rd.  ? 

2.  When  barley  is  worth  25|^  per  bushel,  what  is  the  value 
of  Jbu.?     of  |bu.? 

3.  A  book,  the  retail  price  of  which  was  $5,  was  sold  at 
wholesale  for  ±  of  the  retail  price,  with  ^  off  from  that  for 
cash.     Find  the  selling  price  of  10  books. 


5.  50  x  ^  x  7f  . 

6.  If  x  4|  x  8f  . 
as  much.    How  much 


WRITTEN   EXERCISE 

Reduce  to  their  simplest  form  : 

1.  I  of  |  of  f  3.    71  x  25  x  f  . 

2.  I  of  f  of  21  4.    3|  x  4-J  x  20. 

7.  A  saves  f  9.75  per  week  and  B  f 

more  will  A  have  than  B  at  the  end  of  the  year  ? 

8.  A  merchant  bought  a  piece  of  cloth  containing  43^  yd. 
at  81.50  per  yard.     He  sold  f  of  it  at  11.621  a  yard,  and  the  re- 
mainder at  $1.37|  a  yard.     Did  he  gain  or  lose,  and  how  much? 

The  following  is  a  recent  clipping  from  a  daily  paper.     It  shows  the 
prices  of  corn  on  the  New  York  market. 

NEW  YORK  CORN  QUOTATIONS 


DELIVERY 


PREVIOUS  CLOSING 


HIGHEST 


LOWEST 


CLOSIN 


July 
September 


56-1 


56 


54!* 


55 


9.  D  bought  25,000  bu.  September  corn  at  the  opening 
price  and  sold  it  at  the  highest  price.  What  was  his  gain  ? 
Had  he  bought  at  the  lowest  price  and  sold  at  the  highest 
price,  what  would  he  have  gained? 


130  PEACTICAL   BUSINESS   ARITHMETIC 

10.  E  bought  12,500  bu.  July  corn  at  the  lowest  price  and 
sold  it  at  the  closing  price.     What  was   his    gain  ?      Had    he 
bought  at  the  lowest  price  and  sold  at  the  highest  price,  what 
would  he  have   gained  ? 

11.  A  gold  dollar  weighs  25.8  Troy  grains.     For  every  90 
parts  of  pure  gold  there  are  ten  parts  of  alloy.     How  many 
grains  of  each  kind  in  a  gold  dollar  ?  in  a  5-dollar  gold  piece  ? 

12.  A  5-cent  piece  weighs  77.16  Troy    grains.     For   every 
part  of  nickel  there  are  three    parts    of    copper.     How  many 
grains  of  each  kind  in  a  5-cent  piece  ? 

13.  The  second  general  coinage  act  (1834)  of    the  United 
States  made  one  silver  dollar  weigh  approximately  as  much  as 
sixteen  gold  dollars,  and  this  ratio  of  sixteen  to  one  has  been 
maintained  up  to  the  present  time.       What  is  the  weight  of 
a  silver  dollar  ?      If  silver  coins  are  -f$  pure,  how  much  pure 
silver  in  10  silver  dollars  ? 

SHORT   METHODS  IN  MULTIPLICATION 

182.  When  mixed  numbers  are  large,  they  may  be  multiplied 
as  shown  in  the  following  example. 

183.  Example.     Multiply  255J  by  24f. 

2551 

SOLUTION.    Multiply  the  fractions  together  9^2 

and  obtain  -£%,  which  write  as  shown  in  the  „ 

margin.     Multiply  the  integer  in  the  multi-  1T>  ~ 

plicand  by  the  fraction  in  the  multiplier  and  102       =  |  of  255 

obtain  102.    Multiply  the  fraction  in  the  mul-  8       =24  times  1 

tiplicand  by  the  integer  in  the  multiplier  and  1Q20  1 

obtain  8.     Multiply  the  integers  together  and  ""      I    =  24  times  255 

add   the   partial    products.      The    result   is  ^li 

6230Tv  6230T25  =  24f  times  255J 

WRITTEN  EXERCISE 

Multiply  : 

1.  975£  by  18J.     3.  720J  by  21f .     5.  512^  by  16-J. 

2.  876|  by  21  f     4.  445J  by  46|.     6.  450T^  by  20|. 


COMMON   FRACTIONS  131 


SQUARING   NUMBERS   ENDING   IN   J   OR   5 

184.    Examples.     1.    Multiply  9|  by  9j. 

SOLUTION.     \  of  \  —  £,  which  write  as  shown  in  the  margin.    \          9-i 
of  the  integer  in  the  multiplicand  plus  \  of  the  integer  in  the  multi-          QJ^ 
plier  is  equal  to  either  the  integer  in  the  multiplicand  or  multiplier. 
Therefore,  add  1  to  the  integer  in  the  multiplicand  and  multiply  by  the 
multiplier.    9  x  10  =  90.     Then,  9£  x  9£  =  90|-. 

2.  Find  the  cost  of  8.5  T.  of  coal  at  18.50  per  ton. 

SOLUTION.  The  principles  embodied  in  this  example  are  practi- 
cally the  same  as  those  in  problem  1.  .5  x  .6  =  .25,  8  x  9  =  72. 
Therefore,  8.5  tons  of  coal  at  $8.50  per  ton  will  cost  $72.25. 

3.  Find  the  cost  of  75  A.  of  land  at  1  75  per  acre. 

SOLUTION.     This  problem   is  similar  to  example  2,    the  only  75 

difference  being  in  the  matter  of  the   decimal   point.     Since  the  7^ 

decimal  point  has  no  particular  bearing  upon  the  steps  in  the  pro- 
cess  of  multiplying,  proceed  to  find  the  product  as  in  example  2. 
5  x  5  =  25,  which  write  as  shown  in  the  margin.     7  x  8  =  56,  which  write  to  com- 
plete the  product.     75  acres  of  land  at  $75  an  acre  will  therefore  cost  $5625. 

ORAL   EXERCISE 

Multiply  : 

1.  1|  by  1|,    6.   6  J  by  6J.         ll.  13|  by  13£.  16.   16  J  by  16J. 

2.  2|by2|.     7.   7.  5  by  7.5.      12.  14|  by  14|.  17.  17|  by  17|. 

3.  3lby3|,    8.   8.5  by  8.5.      13.  15J  by  15|.  18.   18J  by  18J. 

4.  41  by  41.    9.  9.5  by  9.5.     14.  11.5  by  11.5.  19.  195  by  195. 
5-  5Jby5f  10.   10.5  by  10.5.  15.  12.5  by  12.5.  20.  205  by  205. 

WRITTEN  EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally. 

1.    Find  the  total  cost  of: 

85  Ib.  of  tea  at  85  f.  55  Ib.  tea  at  55  f. 

75  gal.  sirup  at  75  £  75  bbl.  flour  at  17.50. 

45  gal.  sirup  at  45^.  650  bbl.  oatmeal  at  $6.50. 

2|-  bu.  beans  at  |2.50.  25  doz.  cans  olives  at  §2.50. 

35  gal.  molasses  at  35^.  95  cs.  salad  dressing  at  95^. 

65  cs.  horseradish  at  65  ^.  750  Ib.  cream  codfish  at  7^. 

4J  cs.  baking  powder  at  §4.50.  3J  cs.  baking  powder  at  $  3.50. 


in  the  multiplier  is  equal  to  ^  of  6  +  7,  or  6^,  which  added  to  *>  of  \  rrj 

equals  6|.     Write  f  as  shown  in  the  margin,  and  carry  6.     6x7+6 

=  48.     Therefore,  1\  x  6£  =  48».  ^\ 


132  PRACTICAL    BUSINESS   ARITHMETIC 

MULTIPLICATION    OF   ANY   NUMBERS    ENDING   IN    1   OR    .5 

185.    Examples.     1.    Multiply  7|  by  6J. 

SOLUTION.     \  of  the  integer  in  the  multiplicand  plus  \  of  the  integer  (JX 

the  multiplier  is  equal  to  icr^^     - -1    -1--'-1-    -**-*-     '     -  - 

als  6|.     Write  £  as  shown  ii 

8.     Therefore,  7|  x  6£  =  48 

2.    Multiply  7-1-  by  9J. 

71 

SOLUTION.     \  of  7  +  9  =  8,  with  no  remainder.     |  of  |  =  i,  which  * 

write  as  shown  in  the  margin,  and  carry  8.      7x9  +  8  =  71.     There-  2 

fore,  ?i  x  9| .  =  71 J.  71 J 

Observe  that  :  (1)  in  finding  |  of  any  number  (dividing  a  number  by  2) 
there  is  either  nothing  remaining  or  1  remaining ;  (2)  in  finding  |  of  an 
even  number  there  can  be  no  remainder,  and  in  finding  £  of  an  odd  number 
there  is  always  a  remainder  1.  Hence,  to  multiply  numbers  ending  in  ^  or  .5 : 

Mentally  determine  the  sum  of  the  integers  in  the  multiplicand  and  multiplier. 
If  it  is  an  even  number,  write  \  (.25  or  25}  in  the  product.  If  it  i.s  an  odd  num- 
ber, write  f  (.75  or  75)  in  the  product.  Multiply  the  integers  and  to  the  product 
add  \  of  their  sum. 

ORAL  EXERCISE 

Multiply  : 

1.  3Jby7j.  4.    17|  by  2|,  7.    3.5  by  8.5. 

2.  4£  by  51.  5.    14|  by  6|,  8.    7.5  by  6.5. 

3.  161  by  4J.  6.    211  by  9J.  9.    5.5  by  8.5. 

WRITTEN   EXERCISE 

Make  the  extensions  in  each  of  the  following  problems  mentally. 

1.  Find  the  total  cost  of  : 

6.5  T.  coal  at  18.50.  8.5  T.  coal  at  19.50. 

2.5  T.  hay  at  117.50.  16.5  T.  hay  at  111.50. 

15.5  cd.  wood  at  13.50.  14.5  cd.  wood  at  $5.50. 

2.  Find  the  total  cost  of  : 

45  bu.  beans  at  $2.50.  350  bu.  wheat  at  11.05. 

35  bbl.  flour  at  $6.50.  350  bu.  beans  at  $2.50. 

45  bbl.  flour  at  $8.50.  85  bbl.  oatmeal  at  $7.50. 


COMMON   FRACTIONS  133 


DIVISION 

ORAL   EXERCISE 

1.  8  A.  -s-4  =  ?     8  ninths  (|)  -s-  4  ? 

2.  If  2  Ib.  of  coffee  costs  $0.66f  (If),  what  will  1  Ib.  cost? 
Divide  f  by  2.      What  is  the  effect  of  dividing  the  numerator 
of  a  fraction  ? 

3.  |-i-2  =  ?     Jof|  =  ? 

4.  Because   -|  -t-  2  =  -|-   of   |-,    therefore,  ^  -r-  5  =  ^   of   |,  or 
1*1.     ixi  =  ? 

5.  What  is  the  quotient  of  J  -r-  5  ?     of  £  -s-  8  ?     of  -J  -5-  2  ? 
Because  l  -*-  5  =  ^  of  J,  therefore  |  -;-  5  =  2  times  ^  of  ^. 
is-5  =  lofor      x  i=? 


7.  How  much  is  f  -r-  5  ?     £  -«-  3  ?     7J-  (-^)  ^-  8  ?     3J  -i-  6  ? 

8.  What  is  the  effect  of  multiplying  the  denominator  of  a 
fraction  ? 

186.  In  the  above  exercise  it  is  clear  that 

Dividing  the  numerator  of  a  fraction  by  an  integer  divides  the 
whole  fraction  ;  and, 

Multiplying  the  denominator  of  a  fraction  by  an  integer  divides 
the  whole  fraction. 

ORAL  EXERCISE 

Find  the  quotient  of: 

1.  f-f-4.       4.   |^-12.      7.   ^  +-4.      10.   f-r-9.      13.   -J-s-19. 

2.  ^+-2.      5.   f-12.      8.   ^  +  9.      11.   i^6.      14.   ^  +  5. 

3.  If.  ^5.       6.    T^-3.       9.    T^H-7.       12.    1-5.       15.    ^-5. 

187.  Examples.     1.    Divide  28J  by  7. 

SOLUTION.     First  divide   the  integers  and   the  result  is  4  ;    then  44 

divide    the    fraction     by     7   and     the    result    is    |.        Therefore, 

28|-7  =  4^. 

2.    Divide  26|  by  8. 

SOLUTION.     Divide  26  by  8  and  the  result  is  3  with  a  remainder  2.  3_5_ 

Join  the  remainder,  2,  with  the  fraction,  |,  making  2|.     Reduce  2}  ~ 

to  an  improper  fraction  and  the  result  is  f  .     |  -=-  8  =  T5^.     Therefore, 
26i  -  8  -  3. 


134  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 


Divide  : 

1. 

16* 

by  4. 

5. 

32f 

by  4. 

9. 

21*  by 

8. 

13. 

8* 

by  5. 

2. 

18* 

by  9. 

6. 

27J 

by  7. 

10. 

24f  by 

6. 

14. 

14f 

by  7. 

3. 

25£ 

by  2. 

7. 

19* 

by  9. 

11. 

45fby 

5. 

15. 

11* 

by  9. 

4. 

17* 

by  8. 

8. 

20f 

by  10. 

12. 

40fby 

10. 

16. 

26* 

by  10. 

ORAL  EXERCISE 

1.  How  many  eighths  in  one  ?     1  +  -J  =  ? 

2.  What    is    the    value     of:     1  +  ^?      3  +  *?     17 +  J? 
125-=-TV?     250 +  £? 

3.  Read  aloud  the  following,  supplying  the  missing  word : 
To  divide  an  integer  by  a  unit  fraction,  multiply  the  integer  by 
the of  the  fraction. 

4.  What  is  the  value  of  25  +  *  ?   2.5  +  *?   7.5  +  *?  25.5  + 
j_?  54^1?  48  +  i?  29  +  *?  2*  +  *? 

5.  If  B,  in  the  accompanying  dia- 
gram, is  1,  what   is  0?    How  many 
blocks  like  O'mS?   1  +  *  =  ? 

6.  If  A  is  1,  what  is  B  ?    A  is  how 
many  times  B  ?     That  is,  A  +  B  =  ? 
l+f=?  A 

7.  If  1  + 1  =  f  (1*),  then  2  +  f  =  ? 

8.  What  is  the  value  of  4  +  f  ?   5  +  f?     12  +  -|?   15  +  J? 

9.  Read  aloud  the  following,  supplying  the  missing  words  : 

If  A  is  1,  B  is ,  and  O  is .      If   B   is   contained  in 

A  |  (1*)  times,  it  is  contained  in  0  *  of  |  times  or times. 

That  is,  *  +  f  =  *  x  f  = . 

10.    What  is  the  value  of  *  +  *?     f  +  |?     |-  +  f?     £  +  £? 

188.  The  reciprocal  of  a  fraction  is  1  divided  by  that  fraction. 
Thus,  the  reciprocal  of  f  is  1  -*-  f,  or  |.    That  is,  the  reciprocal  of  a  fraction 

is  the  fraction  inverted. 

189.  Reciprocal  numbers,  as  we  use  the  terms  in  arithmetic, 
are  numbers  whose  product  is  1. 

Thus,  4  and  \,  \  and  f ,  $  and  6,  f  and  f ,  are  reciprocal  numbers,  because 
their  product  is  equal  to  1. 


COMMON   FRACTIONS 


135 


190.  It  has  been  seen  that  the  brief  method  for  dividing  a 
fraction  or  an  integer  by  a  fraction  is  to  multiply  the  dividend 
by  the  reciprocal  of  the  divisor. 

The  principles  of  cancellation  should  be  used  whenever  possible.  Inte- 
gers and  mixed  numbers  should  be  reduced  to  improper  fractions  before 
applying  the  rule. 


Divide : 


WRITTEN  EXERCISE 


1. 
2. 
3. 
4. 
5. 
6. 


4  by  f . 
?l  by  1. 
95  by  f . 
88  by  f . 
16  by  f . 

by'*- 


7. 

8. 

9. 
10. 
11. 
12. 


4f  by  f . 

i9o  by  |. 
6|  by  I*. 
160  by  41. 
250  by  3f . 


13. 
14. 
15. 
16. 
17. 
18. 


191.    Examples.     1.    Divide  2190  by  48|. 

SOLUTION.  Multiplying  both  dividend  and  divisor  by 
the  same  number  does  not  affect  the  quotient ;  hence, 
multiply  the  dividend  and  divisor  by  3  and  obtain  for  the 
new  dividend  and  divisor  6570  and  146,  respectively. 
Divide  the  same  as  in  simple  numbers  and  obtain  the 
result  45.  Or, 

Reduce  both  the  dividend  and  divisor  to  thirds,  obtain- 
ing £537-°  and  i|£.  Reject  the  common  denominators 
and  divide  as  in  whole  numbers. 


2.    Divide 


by  12J. 


SOLUTION.  Multiply  both  dividend  and  divisor  by  6, 
the  least  common  denominator  of  the  fractions,  and  di- 
vide as  in  simple  numbers.  The  result  is  5f  |.  Or, 

Reduce  both  the  dividend  and  divisor  to  sixths,  obtain- 
ing as  a  result  -7/  and  £$*.  Reject  the  common  denomi- 
nator and  divide  as  in  simple  numbers. 


Divide: 

1.  2701  by  12|, 

2.  508^  by  30|. 

3.  14311  by  20|. 


WRITTEN  EXERCISE 


f  by  f 
169  by  4|. 
640  by  5f . 
625  by  831 
920f  by  73. 


48f)2190 

_3 3_ 

146)  6570(45 
584 
730 
730 


121)651 
6       6 


74)393(5ff 
370 
23 


4. 
5. 
6. 


962 1  by  31|, 
650f  by  26i, 
16801  by  45i. 


7. 


7552  by  78| . 

8.  470f  by  17  J. 

9.  1054|  by  1681. 


136  PRACTICAL    BUSINESS   ARITHMETIC 

FRACTIONAL   RELATIONS 

ORAL  EXERCISE 

1.  If  /  in   the  accompanying  diagram  is 
1,  what  is  e?    d?    c?    b?  a? 

2.  What  part  of  e  is/?    of  d?    of  c?    of 
b?    of  a?    What  part  of  6  is  1?    of  5?   of  4  ? 
of  3?    of  2? 

__  3.    What  part  of  a  is  e?    d?    c?    b?    What 

part  of  6  is  2?    3?    4?    5? 

4.  What  part  of  d.isf?     What  part  of  b  is  e?     What  part 
of  1  (f)  is  i  ?     What  part  of  f  is  1  (§)  ? 

5.  What  part  of  7  bu.  is  1  bu.?     What  part  of  7  eighths  (|) 
isl  eighth  (J)? 

6.  What  part  of  |  is  -|? 

SOLUTION,     f  and  f  are  similar  fractions  ;  hence  they  may  be  compared  in 
the  same  manner  as  concrete  integral  numbers.    2  is  f  of  3  ;  therefore,  f  is  f  of 

I;  or, 

fisf  off.    £  =  f  x$  =  f. 


7.  f  is  what  part  of  If  (!)?    of  2|?    of 

8.  |  is  what  part  of  .]  ? 

SOLUTION.     \  —  f.     \  is  \  of  f  ,  therefore,  \  =  %  of  | 


or 


192.  To  find  what  fraction  one  number  is  of  another,  take  the 
number  denoting  a  part  for  the  numerator  of  the  fraction,  and  the 
number  denoting  the  whole  for  the  denominator. 

ORAL   EXERCISE 

1.  If  a  piece  of    work  can    be  performed  in  12    da.,  what 
part  of  it  can  be  performed  in  5  da.  ?  in  7  da.  ? 

2.  If  A  can  do  a  piece  of  work  in  15  da.,  what  part  of  it 
can  he  do  in  1  da.  ?  in  2  da.  ?  in  5  da.  ?  in  7  J  da.  ? 

3.  If  B  can  do  a  piece  of  work  in  7J  da.,  what  part  of  it 
can  he  do  in  1  da.  ?  in  2  da.  ?  in  5  da.  ?  in  5-£  da.  ?  in  6|  da.  ? 


COMMON   FRACTIONS  137 

4.  I  bought  a  farm  for  12000  and  sold  it  for  13000.     What 
part   of   the    cost    was   realized  ?    what  part  of   the  cost  was 
gained  ? 

5.  A  watch  costing  1 75  was  sold  for  $60.     What  part  of 
the  cost  was  realized?     What  part  of  the  cost  was  lost? 

6.  A  and  B  hired  a  pasture  together.     A  pastured  5  cows, 
7  \vk.,  and  B  pastured  7  cows   for  the  same  length  of  time. 
What  part  of  the  price  should  each  pay? 

7.  A  can  do  a  piece  of  work  in  8  da.  which  B  can  do  in  9 
da.     How  many  days  will  it  take  them    if   they  join  in   the 
completion  of  the  work? 

WRITTEN  EXERCISE 

1.  What  part  of  100  is  331?     121?     66f?     8|?     25?     75? 
125?     16 1?     831?     621?     22|?     9T\?     56  J?     6f? 

2.  What  part  of  81  is  33^?     66|^?     25^?     75*?     16$*? 
8$*?    6$*?    3J*>    6J*?    62^?    87J*?    37j*>    14f*? 

3.  What  part  of  1000  is  125?     166$?     666f?     625?     333J? 

4.  Whatpartof  $10  is  13.331?    #1.25?    $1.66f?    $8.331? 
$2.50?     $6.25?     $6.66$? 

5.  A,  B,  C,  and  D  hired  a  pasture  for  $45.     A  pastured  4 
cows  for  4|  mo.;   B,  6  cows  for  3J  mo.;   C,  4  cows  for  1|  mo.; 
D,  5  cows  for  3  mo.     How  much  should  each  pay  ? 

ORAL  EXERCISE 

1.  If  a  in  the  accompanying  diagram  is  10   in.   high,  how 
high    is   b?    c?    dl      10    is    |    of    what    number?   J   of    what 
number?     ^  of  what  number? 

2.  If  225  is  |  of  a  certain  number,  what  is  \  of 
the  number?     |  of  the  number? 

3.  192   is   -|  of   what    number?      ^   of   what 
number?  d  c  b  a 

4.  After  making  a  payment  of  $3500  I  find  that  I  still  owe 
for  |  of  the  cost  of  my  house.    What  was  the  cost  of  my  house? 
How  much  still  remains  unpaid? 


138 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 

1.  The  square  in  the  margin  represents  the 
total  population  of  the  state  of  New  York  (state 
census  of  1905),  and  the  shaded  area  represents 
the  urban  (city)  population.     If  the  suburban 
(country)  population  is  2,420,001,  what  is  the  en- 
tire population  of  the  state  ?  the  urban  population  ? 

2.  In  a  recent  year  the   population   of    Massachusetts  was 
3,002,000,  and  there  were  three  persons  living  in  the  cities  of 
the  state  to  every  one  person  living  in  the  country.     Represent 
this  graphically  as  in  problem  1,  and  find  the  city  population 
and  the  country  population  for  the  state. 


3.  Suppose  that  0  in  the  diagram  represents  the  population 
of  the  United  States  in  1870,  A  the  population  in  1830,  and  F 
the  population  in  1900.     If  the  population  in  1870  was  38,400,000 
(round  numbers),  what  was  the  population  (round  numbers) 
in  1900?     In  1830? 

4.  Suppose  that  F  in  the  diagram  represents  the  population 
of  the  United  States  in  1900,  and  O  the  proportion  of  this  popula- 
tion living  in  cities  in  1900.     What  proportion  of  the  popula- 
tion lived  in  cities  in  1900?     Suppose   that  F  represents  the 
population  in  1860  and  A  the  proportion   of  this  population 
living  in  cities.     Assuming  that  the  city  population  in  1860 
was  5,240,554,  find  the  total  population  for  the  same  year. 

5.  The   total   population   of  New   Jersey    (state   census  of 
1905)  is  2,144,134,  and  the  urban  population,  1,286,480.     Rep- 
resent this  graphically  and  find  the  country  population. 


COMMON    FRACTIONS  139 

CONVERSION   OF   FRACTIONS 

ORAL  EXERCISE 

1.  What  is  the  denominator  of  the  decimal  .6?  of  .75? 

2.  What  is  the  numerator  of  .4?  of  .04?  of  .004?  of  .0004? 

3.  Write  as  a  common  fraction  .7;  .23;  .079;  .0013;  .00123. 

193.  A  decimal  may  be  written  as  a  common  fraction. 

194.  Examples.     1.    Reduce  .0625  to  a  common  fraction. 

SOLUTION.     .0625  means  T$$fo  ;  but  T{fgfo  may  be 


.     .  T          ;          T  _Q_25_  _  _5_  =  _1_ 

expressed  in  simpler  form.     Dividing  both  terms  of  10000        80        16 

the  fraction  by  625,  the  result  is  TV 

WRITTEN  EXERCISE 

Reduce  to  a  common  fraction  or  to  a  mixed  number: 

1.  0.375.  5.   0.9375.  9.    0.0335.  13.  260.675. 

2.  0.0625.         6.   1.66|,  10.   0.00561.         i4.  126.1875. 

3.  0.0016.         7.   0.4375.         11.   181.875.         15.  175.0625. 

4.  0.5625.         8.   0.125.  12.   171.245.         16.  172.0075. 

195.  A  common  fraction  may  be  written  as  a  decimal. 

196.  Example.    Reduce  f  to  a  decimal. 

SOLUTION,     f  equals  £  of  3  units.     3  units  equals  3000  thou-  _ 

sandths.     $  of  3000  thousands  equals  375  thousandths  (.375).  8)3.000 

ORAL  EXERCISE 

1.  Reduce  to  equivalent  decimals  :  £,  \,  f  ,  ^,  f,  J,  f  ,  £,  |  ,  |, 

i<  I'  f  '  t'  lV  T2'  T36'   I'   IT' 

2.  Reduce  to  common  fractions  :   .5,    .25,  .50,  .75,  .33|-,  .66J, 
.16f,  .121,  .6,  .4,  .60,  .40,  .2,  .83J-,  .20,  .081    .375,  .125,  .37  J, 
.87f  .875,  .0625,  .111  .09T\. 

WRITTEN  EXERCISE 
Reduce  to  equivalent  decimals  : 

1.  f         3.    Jff.         5.    yfj.       7.    ?\V        9-    64^0-       u-    21f- 

2.  .       4.    -/5.         6.    fj..        8.    5V        10.    5TL.         12.    165|f 


140  PRACTICAL   BUSINESS   ARITHMETIC 

APPROXIMATIONS 

197.  Since  results  beyond  two  or  three  decimal  places  are 
seldom  required  in  business,  approximations  in   multiplication 
are   frequently    desired.     In   problems   involving  dollars    and 
cents,  it  is  sufficient  to  carry  the  decimal  places  in  the  final 
results  just  far  enough  -to  obtain  accurate  cents.     In  order  to 
make  sure  that  a  product  is  correct  to  the  nearest  cent,  it  is 
usually  necessary  to  carry  the  partial  products  to  three  deci- 
mal places. 

198.  Example.     If    $1    put    at    compound     interest    (see 
page  314)  for  10  yr.  at  4J%  amounts  to  $1.55297,  what  will 
$  4125.67  amdunt  to  in  the  same  time  at  the  same  rate  ? 

•  SOLUTION.      It     has      been      seen      FULL  PROCESS  CONTRACTED  PROCESS 

(page  52)  that  in  multiplying  there  is           -j    c£.>  Q7  i    r  5297 

no  advantage   in   beginning  with   the  ^-.Qr  ^7  /nor  £7 

lowest  order  of  the  multiplier.     In  this  ^ 


example  it  will  be  seen  that  there  is  a  6211.88                            6211.88 

decided  advantage   in  beginning  with  155.297                            155.297 

the  highest  order  of  the  multiplier.  o-i   nrn  A                           o-i 

In  beginning  the  multiplication  note  n  fj£»A 
that  4000  times  .00007  =  .28  and  write 

8  in  the  hundred  ths'  place.     Complete  .931 


and  point  off  the  first  partial  product  .1087079  .109 

as  shown   in   the  process  at  the  left. 


041 


85  7.765 

782  .932 


7399  6407.04 


The  other  partial  products  are    then 
formed  in  natural  order 

The  work  is  given  in  full  and  in  contracted  form.  Examine  both  processes. 
Note  that  in  the  full  process  all  of  the  work  on  the  right  of  the  vertical  line  is 
wasted  ;  also  note  how  much  better  for  practical  purposes  the  contracted  form 
is  than  the  other.  In  this  problem  the  first  two  steps  are  the  same  by  either 
process.  Multiplication  by  20  would  give  a  figure  in  the  fourth  place.  Instead 
of  writing  down  the  product  of  20  times  .00007,  add  the  nearest  ten  to  the  next 
column.  2x9  +  1  =  19;  2  x  2  -f  1  =  5  ;  etc.  In  multiplying  by  the  next  5  it  is 
not  necessary  to  take  the  7  in  the  multiplicand  into  account;  in  multiplying  by 
.6  both  7  and  9  in  the  multiplicand  may  be  rejected  ;  in  multiplying  by  .07,  the  7, 
9,  and  2  in  the  multiplicand  may  be  rejected.  When  any  figure  in  the  multipli- 
cand is  dropped,  it  may  be  marked  off  as  follows:  1.55V2\9X7.  In  finding  the 
sum  of  the  partial  products  do  not  set  down  the  result  for  the  third  decimal 
place,  but  carry  the  nearest  ten  (3)  to  the  second  decimal  place.  The  required 
result  is  finally  found  to  be  $6407.04. 


COMMON    FRACTIONS  141 

199.  Approximations  in  division  are  also  frequently  desired. 

200.  Example.     If  10.134  A.  of  land  cost  1889.26,  what  is 
the  cost  per  acre  ? 

887.75 
10134) $  889260 

8107  =  approximately.       8  times  1013  (4) 

785 

709  =  approximately        7  times  101  (34) 

76 

71  ==  approximately    0.7  times  10  (134) 

5 
5  =  approximately  0.05  times  1  (0134) 

SOLUTION.  Since  the  decimal  point  appears  in  both  dividend  and  divisor,  it 
is  better  to  first  multiply  each  by  such  a  power  of  ten  as  shall  make  the  divisor 
integral.  In  such  problems  as  this  a  result  correct  to  ^0*  ~r 

the   nearest  cent  is  all  that   is  required.      Since  10's  — - 

(an  approximation  for  the  last  two  figures  in  the  divi-    10134)  $  889260 
dend)  divided   by  10000's  (an   approximation   for  the  785 

divisor)  is  less  than  0.01,  the  last  two  figures  of  the  76 

dividend  will   not   affect  the  quotient,  and  they  may  r 

therefore  be  rejected.     Hence,  also,  the  divisor  may  be 

considered  1013  and  may  be  continually  contracted  ;  but  in  multiplying  the 
divisor  by  each  quotient  figure,  mentally  multiply  the  figure  cut  off  and  carry 
the  nearest  ten.  When  a  figure  is  rejected  in  the  divisor,  it  may  be  marked 
off  as  explained  in  §  198.  The  work  may  be  further  abridged  by  omitting  the 
partial  products  and  writing  down  the  remainders  only  as  explained  on  page  67. 

WRITTEN   EXERCISES 

1.  Divide  20,000  by  3.1416  correct  to  .01. 

2.  Find  the  product  of  10.48  x  3.14159  correct  to  two  deci- 
mal places. 

3.  If  fl  placed  at  simple  interest  for  1  yr.  7  mo.  at  3-|  °/0 
will  amount  to  $ 1.05541,  what  will  11869.75  amount  to  in  the 
same  time  at  the  same  rate  ? 

4.  The  estimated  population  of  Continental  United  States 
for  1906  was  92,500,000  and   the  area  was  3,602,990  sq.  mi. 
What  was  the  average  population  per  square  mile  for  this  year, 
to  the  nearest  unit  ? 


142  PRACTICAL   BUSINESS   ARITHMETIC 

THE   SOLUTION   OF   PROBLEMS 

201.  The  steps  in  the  solution  of  a  problem  are  :   (1)  reading 
the  problem  to  find  what  is  given  and  what  is  required;   (2)  de- 
termining from  what  is  given  how  to  find  what  is  required;* 

(3)  outlining  a  process  of  computation  and  then  performing  it; 

(4)  checking  results. 

202.  A  problem  should  be  thoroughly  understood  before  any 
attempt  is  made  to  solve  it ;  and  when  the  relation  of  what  is 
given  to  what  is  required  has  been  discovered,  the  process  of 
computation  should  be  briefly  indicated  and  then  performed 
as  briefly  and  rapidly  as  possible. 

203.  To  insure  accuracy  the  work  should  always  be  checked 
in  some  manner.     If  the  answer  to  the  problem  is  estimated  in 
advance,  it  will  prove  an  excellent  check  against  absurd  results. 

Thus,  42  doz.  boys'  hose  at  $48  a  dozen  is  equal  to  approximately 
40  x  $50 ;  9|%  of  1290  bu.  is  equal  to  approximately  ^  of  1290  bu.  ;  etc. 

204.  Example.    A  tailor  used  30  yd.  of  flannel  in  making  18 
waistcoats  ;  at  that  rate  how  many  yards  will  he  require  in 
making  45  waistcoats  ? 

SOLUTION 

1.  The  quantity  needed  in  making  18  waistcoats  is  given  and  the  quantity 
needed  in  making  45  waistcoats  is  required. 

2.  One  waistcoat  requires  f £  yd. ;  45  waistcoats  will  require  45  times  ff  yd. 
15  5 

3.    — =  75  ;  that  is  75  yd.  of  flannel  are  required   in  making  45 

3 

waistcoats. 

4.  f  §  yd.  =  f  yd.  ;  |4  yd.  =  f  yd.  ;  therefore  the  work  is  probably  correct. 

205.  If  reasons  for  conclusions,  processes,  and  results  are  given, 
they  should  be  brief  and  accurate.     It  is  also  a  mistake  to  try 
to  use  the  language  of  the  book  or  teacher.     Such   artificial 
work  stifles  thought  and  conceals  the  condition  of  the  learner. 

The  subject  of  analysis  should  not  be  unduly  emphasized.  A  correct 
solution  may  generally  be  accepted  as  evidence  that  the  correct  analysis  has 
been  made. 


COMMON   FRACTIONS  143 

ORAL   EXERCISE 

In  the  following  problems  first  find  each  result  as  required,  and  then 
give  a  brief,  accurate  explanation  of  the  steps  taken  in  the  solution.  Do 
not  use  pen  or  pencil. 

1.  If  2  T.  cost  $8,  what  will  5  T.  cost? 

SUGGESTION.  $20;  since  2  T.  cost  $  8,  5  T.,  which  are  2|  times  2  T.,  will 
cost  2 1  times  $8,  or  $20. 

2.  24  is  f-  of  what  number  ?  f  of  what  number  ?  -A-  of  what 

I  O  1  O 

number  ? 

3.  220  is  ^  less  than  what  number?     450  is  |  less  than 
what  number  ? 

4.  A,  having  spent   J  of  his  money,  finds  he  has  $84  left. 
How  much  had  he  at  first  ? 

5.  $124  is  ^  more  than  what  sum  of  money?     $300  is  J 
more  than  what  sum  of  money? 

6.  A  man  sold  -f^  of  an  acre  of  land  for  $35.     At  that  rate 
what  is  his  entire  farm  of  100  acres  worth  ? 

7.  A    man    bought    a    stock   of    goods   and   sold   it   at   ^ 
above  cost.     If  he  received  $275,   what  was  the  cost  of  the 
goods  ? 

8.  B  bought  a  stock  of  goods  which  he  sold  at  ^  below  cost. 
If  he  received  for  the  sale  of  the  goods  $240,  what  was  the  cost 
and  what  was  his  loss  ? 

9.  -j9g  of  the  students  in  a  high  school  are  girls  and  the  re- 
mainder are  boys.     If  the  number  of  boys  is  350,  how  many 
scholars  in  the  school  ? 

10.  A  bought  a  quantity  of  wheat  which  he  sold  at  J  above 
cost.     If  he  received  $300  for  the  wheat,  what  did  it  cost  him 
and  what  was  his  gain  ? 

11.  A  bought  a  quantity  of  dry  goods  and  sold  them  so  as  to 
realize  J  more  than  the  cost.     If  the  selling  price  was  $720, 
what  was  the  cost  and  what  was  the  gain  ? 

12.  D  bought  a  stock  of  carpeting  which  he  was  obliged  to 
sell  at  J  below  cost.     If  he  received  $750  for  the  sale  of  the  car- 
peting, what  was  the  cost  of  same,  and  what  was  his  loss  ? 


144  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN   EXERCISE 

In  the  following  problems  give  both  analysis  and  computation. 

1.  If  1-  Ib.  of  tea  cost  21  £  what  will  9J  Ib.  cost  ? 

COMPUTATION  ANALYSIS 

9£  -  \9-  9|  =  V9-  5  9|  is  therefore  19  times  |.     If  $  Ib.  cost 

19  x  21  ^  =  $3.99       21  ?,  9fc  Ib.  will  cost  19  times  21^,  or  $3.99. 

2.  If  |  of  a  pound  of  tea  cost  42  ^,  what  will  35-J  Ib.  cost  ? 

3.  If  a  drain  can  be  dug  in  17  da.   by  45  men,  how  many 
men  will  it  take  to  dig  ^  of  it  in  3  da.? 

4.  In  what  time  will  3  boys  at  $0.621  per  day  earn  as  much 
as  4  men  at  §2.25  each  per  day  will  earn  in  45 J   da.  ? 

5.  A  spends  $72  per  week  or  |  of  his    income  ;   B    saves 
$48  per  week  or'-|  of  his  income.     How  long  will  it  take  A 
to  save  as  much  as  B  saves  in  five  weeks  ? 

6.  If  115  bbl.   of  wheat  are  required    to  make  23  bbl.   of 
flour,  how  many  barrels  will  be  required  to  make  50  bbl.   of 
flour?  117  bbl.  of  flour?  259  bbl.  of  flour? 

ORAL   REVIEW   EXERCISE 

1.  .05x6x0x2-1-  =  ? 

2.  $0'.75  is  what  part  of  $3? 

3.  What  is  the  sum  of  |>  J,  |,  and  -fa  ? 

4.  Find  the  value  of  .45  +  (.25  x  5)  -  .04. 

5.  60  is  f  of  what  number  ?  f  ?  f  ?   J  ?  f  ? 

6.  At  25?  a  yard,  what  will  2-1  yd.   of  cloth  cost? 

7.  £   is  J  of  what  number  ?     |  is  ^  of  what  number  ? 

8.  If  |  of  an  acre  of  land  costs  $75,  what  will  50  A.  cost  ? 

9.  If  |  of  a  number  is  84,  what  is  5  times  the  same  number  ? 

10.  The  dividend  is  4^  and    the    quotient   is    6f ;   what    is 
the  divisor  ? 

11.  If  6  bu.  of  apples  cost  $15,  what  will    80    bu.  cost  at 
the  same  rate  ? 

12.  At    $460    per    half    mile,   what    will    be    the    cost    of 
grading  6  mi.  of  road  ? 


COMMON    FRACTIONS  145 

13.  How  much  will   4  carpenters   earn    in    10    da.    at    the 
rate  of  12.25  per  day? 

14.  At  $4.50  per  cord,    what  will  be    the    cost    of   4J   cd. 
of  wood  ?  of  6|  cd.  ?  of  12|  cd.  ?  of  7J  cd.  ? 

15.  A  bought  a  horse  for    $96    and    sold    it    for    |    of    its 
cost.     What  part  of  the  cost  was  the  loss  sustained  ? 

16.  A    bought    4^    yd.    of    velvet   at  $5.20  per  yard  and 
gave  in  payment  a  $50  bill.     How  much   change    should   he 
receive  ? 

17.  I  sold  5  A.  of  land  for  $375  and  sustained  a  loss  equal 
to  ^  of  the  original  cost  of  the  land.     What  did  the  land  cost 
per  acre  ? 

18.  D  and  E  agree  to  mow  a  field  for  $36.     If  D  can    do 
as  much  in  2  da.   as  E  can  do  in  3,  how  should    the   money 
be  divided  ? 

19.  N  sold  a  watch    to    O    and    received    1    more    than    it 
cost  him.     If  O  paid  $64  for  the  watch,  what  did  it  cost  N? 
What  per  cent  did  N  gain  ? 

20.  A  earns  $125  per  month.     Of  this  sum  he  spends  $75 
and  saves  the  remainder.      What  part    of    his    monthly  earn- 
ings does  he  save  ?     What  per  cent  ? 

WRITTEN  REVIEW  EXERCISE 

1.  Find  the  cost  of  1100  eggs  at  23|  ^  per  dozen. 

2.  Counting  2000  Ib.  to  a  ton,  find  the  cost  of  5|  T.  of 
steel  at  lT5g  ^  per  pound. 

3.  When  flour  is  sold  at  $6.02  per  barrel  of  196  Ib.,  what 
should  be  paid  for  55J  Ib.  ? 

4.  I  bought  300  bbl.  of  flour  at  $5.75  per  barrel.     At  what 
price  must  I  sell  it  per  barrel  in  order  to  gain  $  150  ? 

5.  The   cost  of    200    bu.  of    wheat    was  $204.50  and    the 
selling  price  $212.35.      What  was  the  gain  per  bushel? 

6.  A  can  do  a  piece  of  work  in  5^  da.   and  B  in  7^  da. 
If  they  join  in  the  completion  of  the  work,  how  long  will  it 
take  them  ? 


146  PRACTICAL   BUSINESS   ARITHMETIC 

7.  How  much  will  7  men  earn  in  6  da.,  working  10  hr.  per 
day,  at  25^  per  hour? 

8.  At  12.50  per  day  of  8  hr.,  how  much  should  a  man 
receive  for  11J  hours'  work  ? 

9.  A  boy  works  4^  da.  at  the  rate  of  $5.75  per  week  of  6 
da.     How  much  does  he  earn  ? 

10.  W,  in  1  of  a  day,  earns  $1.25,  and  Y,  in  |  of  a  day,  earns 
$0.87-|-.     How  much  will  the  two  together  earn  in  40|  da.  ? 

11.  A  and  B    together  can    do  a  piece  of  work    in  10  da. 
If  A  can  complete    the  work  alone  in  16  da.,  how  long  will 
it  take  B  to  do  it? 

12.  Nov.  1,  in  a  recent  year,  was  on  Tuesday.    How  much  did 
B  earn  during  November  if  he  was  employed  every  working  day 
at  the  rate  of  13.75  per  day? 

13.  A    farm   is    divided    into    6    fields    containing,  respec- 
tively, 25f,  26T7g,  32f,  56|,  35T9^,  and  52-^  A.     How  much  is 
the  farm  worth  at  137.50  per  acre? 

14.  Find  the  total  cost  of  :    630  Ib.  sugar  at  4|  ^ ;  375  Ib. 
tea  at  38^;   240  Ib.  crackers  at   5|  ^  ;   65  Ib.  rice  at  7^e  ^ ; 
52J  Ib.  raisins  at  7|  ^ ;  and  250  Ib.  coffee  at  24|  ^. 

15.  A  retailer  bought  5  bbl.  of  flour  at  16.50  per  barrel, 
12  bu.   potatoes  at  75  ^  per  bushel,  and  gave  in  payment  a 
fifty-dollar  bill.     How  much  change  should  he  receive  ? 

16.  Five  garden   lots   measuring    2|,    10 1,    12|,    6T7g,    and 
8T9^  A.  respectively,  were  bought  at    $  212. 87£   per  acre    and 
sold  at  $250.50  per  acre.      Find  the  gain  resulting  from  the 
transaction. 

17.  I  bought  4120  2  yd.  of  silk  at  $1.02  per  yard  and  sold 
|    of   it   at   $1.50   per   yard,    and   the   remainder   for   $1600. 
What   was   the   average    price   received    per   yard,   and    how 
much  did  I  gain  ? 

18.  A,  B,  C,  and  D  hire  a  pasture  for  $419.50.     A  put  in 
25  head   of  cattle   for    4  wk.;  B,  31   head  for  5  wk.;  C,    44 
head  for  6    wk.;    and  D,    40    head   for    8    wk.       How   much 
should  each  be  required  to  pay  ? 


COMMON   FRACTIONS  147 

19.  A  grain  dealer  bought  6750^  bu.  of  corn  at  60^  per 
bushel,  and  2130J  bu.  of  oats  at  32f  f  per  bushel.     He  sold 
the  corn  at  69J  ^  per  bushel,  and  the  oats  at  29f  p  per  bushel. 
Did  he  gain  or  lose,  and  how  much  ? 

20.  A  grocer  bought  15  bbl.  of  molasses,  each   containing 
50  gal.,  at  25|  ^  per  gallon.     He  retailed  150|  gal.   of   it  at 
30^   per   gallon,    170^   gal.   at  28^  per  gallon,   and   the   re- 
mainder   at  35^  per  gallon.      Did  he  gain  or  lose,  and   how 
much  ? 

21.  Find  the  cost  of   25   bx.  of   cheese   weighing :    67  —  4, 
62-4,  61-3,   72-4,  81-5,  64-4,   66-3,   65-5,   61-4, 
62-3,  64-4,   66-3,  65-5,  61-4,   62-3,   64-4,  67-3, 
65-5,  60-3,  62-4,  67-4,  65-4,  60-4,    68-3,    65-4 
lb.,  respectively,  at  11|  ^  per  pound. 

22.  A    dry-goods     merchant     bought     25     pc.    of     Scotch 
cheviot  containing  421,  402,  453,  411,  401,  452,  421,  433,  381, 
351,  362,  41 2,  44 \  452,  391,  371,  422,  47,  41,  421,  433,  401,  471, 
38,  31  yd.,  respectively,  at  39J^  per   yard.      If   he   sold  the 
entire  purchase  at  43f  ^  per  yard,   did  he   gain    or  lose,  and 
how  much  ? 

23.  C.  W.  Bender  fails  in  business.     He  owes  A  1712.25; 
B,  11421. 25;  C,  1625.25;   D,  11460.75;  his    entire    resources 
amount  to  $ 2109. 75.     What  fractional  part  of   his    indebted- 
ness can  he  pay?  what  per  cent?     How  many  cents    on    $1  ? 
If  his  creditors  accept  payment  on  this  basis,  how  much  will 
each  receive  ? 

24.  A    dry-goods    merchant    bought    12    pc.     of    striped 
denim   containing   401,  451,  401,  482,  412,  403,  452,  41  \  44 2, 
392,  511,  38  yd.,  respectively,  at  14|  ^  per  yard;  15  pieces  of 
cashmere  containing  39 \  41 2,  42 \  452,  39,  52,  40,  45,  46,  51, 
472,  42 \  41  \  471,  48  yd.,  respectively,  at  11.12  per  yard;  10 
pc.  wash  silk  containing  35  *,  30,  31 2,  30,  30,  30,  323,  32,  31  *, 
32  yd.,  respectively,  at  31^  per  yard.     He  gave  in  payment, 
cash,  $300,  and  a  60-da.  note  for  the  balance.     What  was  the 
amount  of  the  note  ? 


148 


PRACTICAL    BUSINESS   ARITHMETIC 


25.    Find  the  amount  of  the  following  bill : 

Boston,  Mass.,  Apr.  15,  19 

MESSRS.  CHARLES  H.  PALMER  &  Co. 

Springfield,  Mass. 

Bought  of  EDGAR  W.  TOWNSEND  &  Co. 

Terms :  cash 


250 

Ib.  Rio  Coffee                                          $0.24J 

450 

"    Mocha  Coffee                                         .201 

172 

doz.  Eggs                                                     .14| 

990 

Ib.  White  Sugar                                          .04f 

900 

'     Brown  Sugar                                         .03$ 

975 

1     Granulated  Sugar                                  .06f 

172 

'     Butter                                                     .16$ 

3021 

'     Ham                                                          .131 

280 

'     Cream  Codfish                                       .07| 

11 

pails  Mackerel                                           1.87$ 

120 

Ib.  Raisins                                                    .07f 

480 

"   Starch                                                     .03} 

225 

"   Japan  Tea                                              .26$ 

210 

"   Young  Hyson  Tea                                 .24| 

420 

"   Oolong  Tea                                             .27| 

157 

"   Pearl  Tapioca                                         .03$ 

17 

pkg.  Yeast  Cakes                                      .37$ 

375 

Ib.  Java  Coffee                                            ,23f 

26.  C's  salary  is   $17.50  per  week  of   48    hr.     How  much 
should  he  be  paid  for  11  da.,  working  9  hr.  per  day? 

27.  A   man   earning   $2.75  per   day  of  10  hr.   lost   7-£   hr. 
during  one  week  of  6  da.     How  much  should  he  receive  for 
the  week's  work  ? 

28.  E  begins  work  at  7:30  A.M.  and  quits  work  at  6:30  P.M. 
If  he  is  paid  at  the  rate  of  §3.75  per  day  of  8  hr.  and  he  takes 
the  noon  hour  off  for  lunch,  how  much  should  he  receive  for 
his  day's  labor? 

29.  A  factory  foreman  is  paid  §3.75  per  day  of  8  hr.    and 
$0.50  an  hour  for  overtime.      How  much  should  he  be  paid  for 
a  week  in  which  he  begins  work  at  7  o'clock  A.M.,  quits  work  at 
7:30  o'clock  P.M.,  and  takes  1J  hr.  off  each  day  for  lunch  ? 


COMMON    FRACTIONS 


149 


30.  Copy  the  following  time  sheet  and  find :  (a)  the  total 
number  of  hours  worked  on  each  order ;  (b)  the  total  number 
of  hours  worked  each  day;  (V)  the  amount  earned  on  each 
order ;  and  (<i)  the  total  amount  earned  during  the  week. 

BOSTON   ELEVATED   RAILWAY   CO. 

Time  worked  by  E.  M.  Doe,  during  the  week  ending  Aug.  15. 
Rate  per  hour,  25  cents.     Occupation,  Lineman. 


Order  No. 

Sat. 

Sun. 

Mon. 

Tues. 

Wed. 

Thurs. 

Fri. 

Total 
Hours 

Amount 

420 

21 

41 

715 

2* 

9^ 

960 

7- 

318 

4f 

H 

420 

2i 

4¥ 

H 

715 

4| 

7* 

Total  hr. 

31.  A  foreman  in  a  shoe  factory  receives  $5  per  day  and 
10.50  per  hour  for  overtime.     His  time  for  two  weeks  is  as  fol- 
lows :   Monday,  10£  hr.  ;   Tuesday,  12  hr.  ;   Wednesday,  8  hr.  ; 
Thursday,  8|  hr. ;  Friday,  12^  hr. ;  Saturday,  10  hr. ;  Monday, 
11  hr. ;  Tuesday,  12J  hr. ;  Wednesday,  10  hr. ;  Thursday,  8  hr. ; 
Friday,  8|  hr. ;   Saturday,  9J  hr.     How  much  should  he  be  paid 
for  the  two  weeks'  work,  assuming  that  a  day's  work  is  8  hr.? 

32.  The   following  is  a   manufacturer's    piece-labor  ticket. 
Copy  it  and  find  the  totals  and  amounts  as  indicated. 


PIECE     LA  BO  R 


Workman's  No. 
Week  ending 


/y 


Examined  by 


Articles 

M. 

T. 

w. 

T. 

F. 

s. 

Total 

Price 

Extensions 

Amount 

-^^JJ^ 

,/^ 

^ 

^ 

yX* 

^/-v 



^£J^£ 

//^ 

?  /7 

^  x7 

/z 

/j^^ 

-ft^^g^ 

^r 

2-t?  fa  9- 

T^^J 

/^ 

/fY*< 

CHAPTER  XIII 

ALIQUOT   PARTS 

206.    An  aliquot  part  of  a  number  is  a  part  that  will  be  con- 
tained in  the  number  an  integral  number  of  times. 

Thus,  2£,  3|,  and  5  are  aliquot  parts  of  10. 
ORAL  EXERCISE 

1.  How  many  cents  in  ||  ?  in  $1?  in  $£?  in 

2.  What  aliquot  part  of  $1  is  25^?  50^?  6| 

3.  Read  aloud  the  following,  supplying  the  missing  terms: 
16  x  50^  =  16  x  $|  =  |  of  116  ;l  16  x  25^  =  16  x  $-*-  -  \  of  $16  ; 
16  x  12^=16  x$-  -of  $16;  16x6^=16x$- 

—  of  116. 

4.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  50^;   25^;   12|^;  £>\<f. 

5.  What  is  the  cost  of  160  yd.  of  dress  goods  at  $1?  at 
at  25^?  at  12^?  at  6|^? 

6.  How  many  cents  in  |J?  in  |1?  in  IjL?  in  1^?  in 


7.    What  aliquot  part  of  |1  is  33^? 


8.  Read  aloud  the  following,  supplying  the  missing  terms  : 
l4f^  =  140  x  *i  -  \  of  $140;   90  x  6f0  =  90  x  $- 

=  -  -ofi90;   90x20^  =  90x*  -  =  -  of  $90. 

9.  Read  aloud  the  following,  supplying  the  missing  terms  : 
240x33^=240x1  -  =  J    of    $240  :    240  x  16f  =  240  x 
$1  =  -    -  of  $  240;   240  x  12^  =  240  x  $-  -  of  $  240. 

10.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  33  J^  ;    16|Y;   8J^;   6|^;   14f-^. 

11.  Find  the  cost  of  960yd.  of  cloth  at  33^;  at  16|^;  at 

150 


ALIQUOT   PAKTS  151 

ORAL   EXERCISE 

State  the  cost  of: 

1.  240  Ib.  tea  at  50^;  at  33^;  at  25^. 

2.  B601b.  coffee  at  33^;  at  26^;  at  20  j^;  at!2i?. 

3.  720  gal.  cider  at  6^?;   at6f?;  at  10?';  at  12^?. 

4.  2400  doz.  eggs  at  12*  ?;  at  16f  ?;  at  20?;  at  25?. 

5.  2400  yd.  prints   at  8^?;  at  6f  ?  ;  at  6J?;  at  12-|?. 

6.  960  yd.  cotton  at  6|?;  at8J?;  at6f?;   at  10?;  at!2i?. 

7.  2040yd.  plaids  at  50^;  at  33J?;  at  25?;  at  20?;  at  16f  ?. 

8.  480  Ib.  lard  at  81?;  at  6^?;  at  121?;  at  16f  ?;  at  10^. 

9.  3600  Ib.  raisins  at  12^;  at!6|^;  at  20^;  at  25^;  at  331^. 

10.  480yd.  lining  at  8^;   at  6^  ;  at  10^;  atl2-|^;  at6|^. 

11.  4200  yd.  silesia  at  10^;  at  20^ ;  at  12-J^;  at  16|^ ;  at  14| \f. 

12.  1500  yd.  plaids  at$l ;  at  50^;  at  33^;   at  25^;  at  20^. 

13.  420yd.  stripe  at  10^;  atl2^;  at  14|^;  at  16f  ^;  at  25?. 

14.  120yd.  gingham  at  8J^;  at6J^;  at6f^;  at  loV;  atl2-|-^. 

15.  1240  yd.  wash  silk  at  25^;  at  50^;  at  33^;  at  20?. 

16.  At  the  rate  of  3  for  50^,  what   will  27  handkerchiefs 
cost? 

17.  At  33^?  per  half  dozen,  what  will  12  doz.  handkerchiefs 
cost?  17  doz.?  25  doz.?  7£  doz.?  4|  doz.? 

18.  A  merchant  bought  cloth  at  33 J?  per  yard  and  sold  it 
at  50^  per  yard.     What  was  his  gain  on  1680  yd.? 

ORAL   EXERCISE 

1.  What  is  the  cost  of  12*  yd.  of  silk  at  96  ^  per  yard? 

SUGGESTION.  The  cost  of  12|  yd.  at  96^  =  the  cost  of  96  yd.  at  12^. 
Interchanging  the  multiplicand  and  multiplier  considered  as  abstract  numbers 
does  not  affect  the  product. 

2.  Find  the  cost  of  25  yd.  of  silk  at  $1.72  per  yard. 
SUGGESTION.     The  cost  of  25  yd.  at  1 1 .72  (172^)  =  the  cost  of  172  yd .  at  25^. 

3.  Find  the  cost  of : 

a.  25  yd.  at  16?.       c.    Q\  Ib.  at  32?.       e.    25  yd.  at  84?. 

b.  12lyd.  at  48?.     d.    12|lb.at80^.      /.    12J  yd.  at  |1.75. 


152  PKACTICAL   BUSINESS   ARITHMETIC 

TABLE  OF  ALIQUOT  PARTS 


Nos. 

1'e 
2  8 

i's 

¥* 

iV* 

V* 

r; 

rVs 

iV* 

r« 

ftr's 

1 

.50 

.25 

•121 

.06£ 

.331 

.16f 

.081 

.06| 

.20 

.10 

10 

5. 

H 

H 

.62J 

** 

If 

.831 

.66f 

2. 

1. 

ICO 

50. 

25. 

l*i 

<H 

88J 

l(5f 

B| 

O* 

20. 

10. 

1000 

500. 

250. 

125. 

621 

333$ 

166$ 

831 

66| 

200. 

100. 

WRITTEN  EXERCISE 

In  the  three  problems  following  make  all  the  extensions  mentally. 

1.  Without -copy  ing,  find  quickly  the  total  cost  of  : 
84  Ib.  tea  at  50^.  6^  Ib.  tea  at  64^. 

75  Ib.  tea  at  33J^.  25  Ib.  cocoa  at  52^. 

72  Ib.  coffee  at  25^.  12|  Ib.  cocoa  at  48^. 

84  Ib.  coffee  at  33^.  360  Ib.  codfish  at  6|^. 

25  Ib.  coffee  at  28^.  66  Ib.  crackers  at 

88  Ib.  candy  at  12^.  25  Ib.  chocolate  at 

24  Ib.  tapioca  at  6|^.  25  cs.  horseradish  at 

2.  Without  copying,  find  quickly  the  total  cost  of: 

25  yd.  silk  at  8 
12|  yd.  silk  at 
750  pc.  lace  at  6^ 
112  yd.  ticking  at 
210  yd.  plaids  at 

128  gro.  buttons  at  12|  ^. 
68  yd.  lansdowne  at 


77  yd.  duck  at 
6^  gro.  buttons  at  32^. 
155  yd.  cheviot  at  2 
96  yd.  gingham  at 
84  yd.  shirting  at  12. 
25  doz.  spools  thread  at  2 
168  yd.  striped  denim  at  8J  ^. 
3.    Without  copying,  find  quickly  the  total  cost  of : 

25  bu.  corn  at  $0.84. 
25  bu.  corn  at  $0.44. 
25  bu.  oats  at  $0.35. 
121  bu.  rye  at  $1.04. 
6|  bu.  wheat  at  $1.20. 
6|  bu.  wheat  at  $1.12. 
25  bu.  timothy  seed  at  $2.40. 
50  bu.  timothy  seed  at  $2.75. 


25  bu.  corn  at 
25  bu.  corn  at  -10.72. 
12-J  bu.  oats  at  10.36. 
25  bu.  beans  at  82.80. 
12|-bu.  wheat  at  -fl.04. 
12Jbu.  millet  at  $1.24. 
25  bu.  clover  seed  at  13.60. 
50  bu.  clover  seed  at  13.75. 


ALIQUOT   PARTS  153 

ORAL  EXERCISE 

1.  Multiply  by  10:  4;  15  ;  .07  ;  8^;  $1.12  ;  $  24.60;  112.125. 

2.  Multiply   by    100:    3;    17;     .09;    12^;    $1.64;    121. IT. 

3.  Multiply   by   1000:   7;    29;    .19;    15^;  11.75;    123.72. 

4.  What  aliquot  part  of  $10  is  12.50?     Find  the  cost  of  16 
articles  at  $10  each ;  at  12.50  each. 

5.  Find  the  cost  of  84  bu.  of  wheat  at  11.25. 

SOLUTION.    §1.25  is  $  of  $10.   84  bu.  at  $10  =  $840;   £  of  $840  =  $105. 

6.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  $1.25. 

SOLUTION.    $1.25  is  |  of  $10;  hence,  multiply  the  quantity  by  10  and  take  \ 
of  the  product. 

7.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  $2.50;  $3.33£;    |1.66f. 

8.  Find  the  cost  of  168  yd.  of  cloth  at  $1.25;  at  $2.50; 
at  $3.331;   at  $1.66|. 

9.  What  aliquot  part  of  $100  is  $25  ?    $12.50?   $6.25  ? 

10.  Find  the  cost  of  72  chairs  at  $25  each. 

SOLUTION.    72   chairs   at  $100  =  $7200;  but  the  price  is  $25,  which  is  £  of 
$100  ;  therefore,  \  of  $7200,  or  $1800,  is  the  required  cost. 

11.  Give  a  short  method  for  multiplying  any  number  by  25 ; 
by  12|;   by  6-1;  by  331;   by  8J. 

12.  Find  the  cost  of  25  T.  coal  at  $7.20 ;  of  6|  T. ;  of  121  T. 

13.  What  aliquot  part  of  1000  is  250?    500?    125?    621? 
3331?    166f?    200?    100?    83i?    66f? 

14.  Formulate  a  short   method  for    multiplying  a    number 
by  250. 

SOLUTION.   Since  250  =  101°~,  multiply  by  1000  and  take  £  of  the  product. 

15.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  $125;  $166|. 

16.  Multiply  84  by  50;  by  25;  by  121;  by  16f ;  by  331 

17.  Multiply  160  by  21;  by  11;  by  121 ;  by  125;  by  62-|-. 

18.  Multiply  240  by  3| ;  by  If;  by  331;  by  16|;  by  3331. 


154  PEACTICAL   BUSINESS   ARITHMETIC 

19.  Find  the  cost  of  250  sofa  beds  at  §32  each. 

SOLUTION.  The  cost  of  250  beds  at  $32  —  the  cost  of  32  beds  at  $250.  The 
cost  of  32  beds  at  .$1000  =  $32,000  ;  but  the  price  is  $250,  which  is  \  of  $  1000 ; 
therefore,  \  of  $32,000,  or  $8000,  is  the  required  cost. 

20.  Find  the  cost  of  720  couches  at  $12.50  each. 

21.  Find  the  cost  of  440  Ib.  sugar  at  2^. 

SOLUTION.  2^  is  i  of  10^.  The  cost  of  440  Ib.  at  10^  =  $44 ;  but  the  price  is 
2^,  therefore,  \  of  $44,  or  $11  —  the  required  cost. 

22.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  1-J^. 

SOLUTION.  \\<f>  =  \  of  10^ ;  hence,  point  off  one  place  in  the  quantity  and  take 
\  of  the  result. 

23.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  2|^;   3J^  ;   1|^. 

24.  Find    the    cost    of    180  Ik    at    2^;    at    l\f  \    at 
at  1J^.     Also  of  240  Ib.  at  each  of  these  prices. 

25.  Find  the   cost   of    2400    Ib.   at    2|  ^;     at    1^;    at 
at  If  ^.     Also  of  360  Ib.  at  each  of  these  prices. 

ORAL    EXERCISE 

By  inspection  find  the  cost  of: 

1.  25  Ib.  tea  at  54^.  16.   1-J  yd.  silk  at  88^. 

2.  25  Ib.  tea  at  33 j£  17.   64  pc.  lace  at  $1.25. 

3.  125  Ib.  tea  at  64^.  18.   125  yd.  silk  at  11.12. 

4.  6-|  A.  land  at  1112.  19.   1250  bbl.  beef  at  124. 

5.  25  T.  coal  at  18.40.  20.   78  yd.  velvet  at  $2.50. 

6.  25  T.  coal  at  15.20.  21.   2|  bu. -potatoes  at  44^. 

7.  18  T.  coal  at  16.25.  22.  640  bu.  apples  at  12\f. 

8.  164  A.  land  at  825.  23.   840  yd.  prints  at  16| f. 

9.  72  T.  coal  at  $6.25.  24.   12|  bu.  potatoes  at  64^. 

10.  250  yd.  silk  at  88^.  25.  84lbookcases  at  812.50. 

11.  250  yd.  silk  at  96^.  26.  810  bbl.  pork  at  812.50. 

12.  25  pc.  lace  at  86.60.  27.  125  yd.  crepon  at  §3.60. 

13.  250  yd.  silk  at  f  1.12.  28.  12-J-  yd.  cheviot  at  81.04. 

14.  192  A.  land  at  812.50.  29.  24 "oak  sideboards  at  8125 

15.  165  gro.  buttons  at  33^.  30.  12^  yd.  gunner's  duck  at 


ALIQUOT   PARTS  155 

WRITTEN    EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally.    See 
how  many  of  the  problems  can  be  done  in  10  minutes. 

1.  Without  copying,  find  the  total  cost  of  : 

425  Ib.  at  10  f.            2500  Ib.  at  64  £  24  Ib.  at  11  f. 

310  Ib.  at  20  £            1600  Ib.  at  25  f.  48  Ib.  at  21  t. 

100  Ib.  at  14  f.  1893  Ib.  at  31  £  21  Ib.  at  96  £ 

1000  Ib.  at  27  £  2500  Ib.  at  14  £  125  Ib.  at  24  £ 

1000  Ib.  at  41  f.  1400  Ib.  at  25  f.  192  Ib.  at  3J  £ 

1250  Ib.  at  44  £  1250  Ib.  at  88  f.  88  Ib.  at  121  £ 

2.  Without  copying,  find  the  total  cost  of  : 

88  yd.  at  11  f.            174   yd.  at  10  f.  24  yd.  at  12  t. 

72  yd.  at  31  £  123  yd.  at  11  £  78  yd.  at  3£  £ 

104  yd.  at  2|  £  127  yd.  at  11  f.  165  yd.  at  20  £ 

480  yd.  at  6|  X.  246  yd.  at  25^.  114  yd.  at  6f  £ 

360  yd.  at  8 J  A  1712  yd.  at  10  £  1280  yd.  at  61  f. 

121  yd.  at  11  £  1783  yd.  at  1.0  X.  192  yd.  at  33^. 

3.  Copy  and  find  the  total  cost  of  : 

450  Ib.  at  1 1  f.             249  Ib.  at  25  f.  6J  Ib.  at  88  f. 

820  Ib.  at  11  f.  240  Ib.  at  3J  £  92  Ib.  at  2|  f. 

1200  Ib.  at  4J  f.  200  Ib.  at  3-|  f.  121  Ib.  at  24  <?. 

1400  Ib.  at  6i  £  450  Ib.  at  6f  £  18  Ib.  at  4  J  f. 

7961  Ib.  at  50  f.  79 J  Ib.  at  40  f.  125  Ib.  at  18  £ 

1293  Ib.  at  30  £  78J  Ib.  at  50  f.  .  648  Ib.  at  6J  ^. 

1480  Ib.  at  40  f.  750  Ib.  at  33J  £  1900  Ib.  at  4J  £ 

4.  Copy  and  find  the  total  cost  of  : 

750  gal.  at  8-J  £             99  gal.  at  30  f.  360  gal.  at  5  f. 

488  gal.  at  6|  f.             60  gal.  at  6|  <f.  625  gal.  at  64  f. 

640  gal.  at  6-[  f.             50  gal.  at  76  ^.  810  gal.  at  1^. 

194  gal.  at  50  f.             25  gal.  at  74  f.  920  gal.  at  2J  £ 

176  gal.  at  25  f.           12 j  gal.  at  88  £  165  gal.  at  6|  f. 

280  gal.  at  12£  £           79  gal.  at  331  £  240  gal.  at  621  ^ 

720  gal.  at  331  £            20  gal.  at  11.79.  666  gal.  at  66|  f. 

366  gal.  at  16  j^.            61  gal.  at  $1.96.  1680  gal.  at  16f  £ 


156  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL   EXERCISE 

1.  How  much  less  than  §1  is  75^?  what  fractional    part 
of  |1  less? 

2.  Find  the  cost  of  144  pc.  of  lace  at  75  ^  per  piece. 

SOLUTION.     At  $  1  per  piece  the  cost  would  be  $  144  ;  but  the  cost  is  not  $  1 
but  ^  less  than  $  1.     Deducting  £  of  $  144,  the  result  is  $  108,  the  required  cost. 

3.  Find  the  cost  of  124  bookcases  at  $7.50. 

SOLUTION.     $7.50  is  \  less  than  $10.     $1240   less    \   of    itself  =  $930,   the 
required  result. 

4.  Formulate  a  rule  for  multiplying  a  number  by  .75;  by 
7  i  ;  by  75 ;  by  750. 

5.  How  much  more  than  $1  is  |1.12|?     What  fractional 
part  of  $  1  more  ? 

6.  Find  the  cost  of  84  yd.  of  silk  at  $1.16f  per  yard. 

SOLUTION.     At  $  1  per  yard,  the  cost  would  be  $84  ;  but  $1.16f  is  £  more 
than  $1.     Adding  \  of  $84  to  itself,  the  result  is  §98,  the  required  cost. 

7.  Formulate  a  short  method  for    finding    the    cost  when 
the     quantity  is   given    and    the    price    is    $1.12^;     $1.16| ; 
$1.33j;  $11.25;  $112.50. 

8.  How    much    less    than    $1    is    87|^?  what    fractional 
part  of  $1  less?     Formulate  a  short  method  for  multiplying  a 
number  by  87|. 

9.  Formulate  a  short  method    for    multiplying    a    number 
by  .831;  by  1.25. 

10.    Compare  the  cost  of  87J  yd.  at  64^  with  the  cost  of 
64  yd.  at  87|^. 

ORAL  EXERCISE 

State  the  cost  of: 

1.  24  yd.  at  75 1.  7.    87 \  yd.  at  $  2.88.  13.      270  yd.  at  111  ^ 

2.  75 yd. at  24^.  8.      25yd.at4^.        14.      144yd.atll^. 

3.  192yd.  at  871^.  9.  28  yd.  at  7-^.  15.  lllyd. 

4.  240yd.  at  831^.  10.  27yd.  at  75^.  16.  1125  yd.  a 

5.  871  yd.  at  $2.48.  11.  75yd.at81^.  17.  1125yd.at32^. 

6.  176  yd.  at  $1.121.  12.  75yd.  at  16^.  18.  1125  yd.  at  48^. 


ALIQUOT   PAKTS 


157 


72yd.  at 

87iyd.  at  88^. 
320yd.  at  11  £ 


WRITTEN  REVIEW  EXERCISE 

1.  Find  the  total  of  the  costs  called  for  in  problems  1—15  in 
the  oral  exercise  at  the  top  of  page  151. 

2.  Find  the  total  cost  of  the  items  in  the  oral  exercise  at  the 
bottom  of  page  154;  of  the -items  in  the  oral  exercise  at  the 
bottom  of  page  156. 

3.  Find  the  total  cost  of  : 

84  yd.  at  if.  98  yd.  at  9^. 

112|  yd.  at  5^.  79  yd.  at  11^. 

112|  yd.  at  Q^  17  yd.  at  16^. 

4.  Find  the  total  cost  of : 

71  yd.  at  22^.  85  yd.  at  30^. 

31yd.  at  44^.  17  yd.  at  25^. 

82yd.  at  88^.  121  yd.  at  39^. 

71  yd.  at  72^.  250  yd.  at  64^. 

5.  Find  the  total  cost  of  : 

192  Ib.  at  31^.  167  Ib.  at  I2£>. 

384  Ib.  at  6-i  f.  184  Ib.  at  37^. 

378  Ib.  at  6\f.  2164  Ib.  at  2-|  f. 

149  Ib.  at  6J  f.  1369  Ib.  at  2 1  f. 

6.  Copy  and  find  the  amount  of  the  following  bills,  less  3  % 

a. 

Rochester,  N.Y.,  Aug.  2,  19 


30yd.  at 
24  yd.  at 
56yd.  at 
124yd.  at  il.l2|. 


1151f  Ib.  at 
17211  Ib.  at 
29111  Ib.  at 
2706  Ib.  at  33 


MR.  C.  G.  GARLIC 

North  Rose,  N.Y. 

Terms  :  cash,  less  3  %. 


To  SMITH,  PERKINS  &  Co.,  Dr. 


330  Ib.  Granulated  Sugar                     6£  0 
32    '    Butter                                        22^ 
64    <     Cheese                                        16f? 
75   '    Young  Hyson  Tea                    24  ^ 
155   '    Dried  Apples                               8^ 
300   '     Brown  Sugar                             3^ 
60   '    Oolong  Tea                                51  ? 
125   '    Rio  Coffee                                  28^ 
250   *    Mocha  Coffee                            24^ 

158 


PEACTICAL   BUSINESS   ARITHMETIC 


b. 


Buffalo,  N.Y.,  Aug.  5,  19 


MR.  GEORGE  A.  COLLIER 

Savannah,  N.Y. 

Bought  of  GEORGE  H.  BUELL  &  Co. 

Terms  :  cash,  less  3  %. 


72  pr.  Boys'  Hose                                  12  tf 
18  doz.  Linen  Handkerchiefs               2.50 
18    "      Lace  Handkerchiefs                 3.33£ 
78  yd.  Silk  Velvet                                 3.331 
75  pc.  Black  Ribbon                             28^ 
347  yd.  Pontiac  Seersucker                    6\f> 
186   "    Washington  Cambric                12ty 

ORAL  EXERCISE 

1.  At  33|  ^  per  pound,  how  many  pounds  of  coffee  can  be 
bought  for  $12? 

SOLUTION.  .33£  =  $  i  ;  3  pounds  can  be  bought  for  $  1  ;  then,  12  x  3  Ib. 
=  36  Ib.,  the  required  result. 

2.  When  the  cost  is  given  and  the  price  is  25^,  how  may 
the  quantity  be  found? 

SOLUTION.  When  the  price  is  25  $ ,  the  quantity  is  4  times  the  cost ;  hence, 
multiply  the  cost  by  4. 

3.  Give  a  short  method  for  finding  the  quantity  when  the 
cost  is  given  and  the  price  is  20^;   33^;   12-^;   &|^;   6|Y; 

4.  Formulate  a  short  method  for  dividing  any  number  by 
125. 

SOLUTION.  125  is  \  of  1000  ;  then  the  quotient  by  125  will  be  8  times  the 
quotient  by  1000.  Therefore,  divide  by  1000  and  multiply  the  result  by  8.  Or, 
T^  =  ToW  Therefore,  multiply  by  8  and  move  the  decimal  point  three 
places  to  the  left. 

5.  Give  a  short  method  for  dividing  by  6^. 

SOLUTION.  6£  =  T\  of  100  ;  then  the  quotient  by  6|  will  be  16  times  the 
quotient  by  100.  Therefore,  move  the  decimal  point  two  places  to  the  left  and 
multiply  the  result  by  16.  Or,  £  =  ^.  Therefore,  multiply  by  16  and  move  the 
decimal  point  two  places  to  the  left. 


ALIQUOT  PARTS 


159 


6.  Give  a  short  method  for  dividing  a  number  by  12 1  ;  by 
16| ;  by  381 .   by  6| ;   by  66|;  by  3331;  by  166|. 

7.  Formulate  a  short  method  for  dividing  a  number  by  .75. 

SOLUTION.  .75  increased  by  ^  of  itself  —  1.  When  the  divisor  is  1  the  quo- 
tient is  the  same  as  the  dividend.  Hence,  to  divide  a  number  by  .75  increase 
the  number  by  %  of  itself. 

8.  At  75^  per  bushel,  how  many  bushels  of  wheat  can  be 
bought  for  $144?  for  $192?  for  $240?  for  1780?  for  11260? 
for  8360?  for  1 1350?  for  1810? 

9.  At  17.50  per  dozen,  how  many  dozen  men's  gloves  can 
be  bought  for  11440? 

SOLUTION.  $7.50  -f  1  of  itself  =  10.  To  divide  by  10  is  to  point  off  one 
place  to  the  left.  $  1440  +  *  of  itself  =  $  1920  ;  $  1920  -=-  $  10  =  192,  the  number 
of  pairs  of  gloves. 

10.  State  a  short  method  for  dividing  a  number  by  7J ;  by 
75 ;  by  750. 

ORAL    EXERCISE 

Find  the  quantity: 


COST 


PRICE  PER 
YARD 


1. 
2. 
3. 
4. 
5. 
6. 


$250 
$120 
8215 
$126 
$125 


7. 

8. 

9. 
10. 
11. 
12. 


COST 

$75 
$12 
$25 
$38 

$125 
$420 


PRICE  PER 
POUND 


If* 


$1.25 


WRITTEN   EXERCISE 


Find  the  quantity : 

PRICE  PER 
COST  YARD 

$570.00  75* 


$612.00 

$274.50 
$281.50 
$864.50 


75^ 


6. 
7. 
8. 
9. 
10. 


COST 

$1721.00 
$1842.50 

$1785.50 
$2142.00 

$2720.50 


PRICE  PER 
BUSHEL 


871* 


CHAPTER   XIV 

BILLS   AND  ACCOUNTS 
BILLS 

207.  A  detailed  statement  of  goods  sold,  or  of  goods  bought 
to  be  sold,  is  called  either  a  bill  or  an  invoice.     A  detailed  state- 
ment of  goods  bought  to  be  used  or  consumed,  such  as  office 
furniture,  stationery,  and  fuel,  or  a  statement  of  services  ren- 
dered, or  of  a  work  performed,  is  called  a  bill. 

Thus,  a  physician's  statement  of  services  rendered,  or  a  transportation 
company's  bill  for  work  performed,  and  the  charges  for  the  same,  is  called  a 
bill ;  but  a  statement  of  a  quantity  of  silk  bought  or  sold  by  a  dry-goods 
merchant  in  the  course  of  trade  is  called  either  a  bill  or  an  invoice. 

208.  The  models  following  show  a  variety  of  current  prac- 
tices in  billing.    They  will  therefore  be  found  helpful  as  studies. 

1.    GROCERIES 
Boston,  Mass.,         Oct.    15,          19 

Messrs.   SMITH,    PERKINS  &  CO. 

Rochester,    N.Y. 

Bought  of  E.  E.  GRAY  COMPANY 

Terms  30  days  Telephone,  Main  167 


3 

bbl.  Rolled  Oats           $6.25 

18 

75 

10 

"   Gold  Medal  Flour       6.50 

65 

00 

5 

bx.  Wool  Soap              3.10 

15 

50 

99 

25 

This  is  one  of  the  simplest  bill  forms;  it  is  the  form  that  is  common 
in  a  great  many  lines  of  business. 


160 


BILLS   AND   ACCOUNTS 


161 


2.    GROCERIES 
Boston,  Mass.,         Nov.    12,  19 

Messrs.    E.    0.    Sherman  &   Co. 

Charlestown,   Mass. 

Bought  of  S.  S.  PIERCE  COMPANY 

Terms  30   da.  ;    3%   10   da. 


10  Red  Label  Hams 
20  mats  Java  Coffee  1500 
12  6-lb.  tins  Mustard  72 
15  6-lb.  tins  Cocoa  90 


146   Ib.      $0.23      $33.58 


.25   375.00 

.36   25.92 

.34   30.60 

$465.10 


Goods  bought  by  the  mat,  chest,  case,  etc.,  are  frequently  billed  by  the 
pound.  The  above  bill  shows  the  form  in  such  cases. 

8.    HARDWARE 

The  following  bill  is  sometimes  used  in  the  hardware  business.  The  first 
number  after  the  name  of  the  article  is  the  quantity;  the  number  above  the 
horizontal  line  following,  the  price  ;  and  the  number  below  the  line,  the  grade. 
Thus,  the  first  item  in  the  bill  shows  that  12  doz.  porcelain  knobs  in  all  were 
sold,  of  which  6  doz.  were  No.  8  at  $1,25  and  6  doz.  No.  16  at  $  1.331. 


19- 


^     °  / 


fbureka   J^arctivare  Qompany 


/  2- 


AL 


> 


162 


PRACTICAL    BUSINESS   ARITHMETIC 
4.    WHOLESALE   DRY   GOODS 

CHICAGO,- 


M 


19. 


Bought  of  MARSHALL  FIELD  &  CO. 

Franklin  Street  and  Fifth  Avenue 


TERMS 


z^ 


jf-rri^^&S^eXs*?  ^4~ 


AZ. 


4-0     37*     40  •>/#•£ V    -^7>    VJ-* 


& 


rfcrf^W^fr^r^, 


4-2. 


J&. 


*2& 


LZ. 


/2 


42-     40 


/^/ 


2^2,^2. 


37%+ 


37 


In  the  wholesale  dry-goods  business  the  price  is  generally  for  a  yard,  and 
the  number  of  yards  to  the  piece  varies  in  some  kinds  of  cloth.  The  first 
item  in  the  above  bill  is  followed  by  a  series  of  numbers,  41,  42,  etc. ;  these 
represent  the  number  of  yards  in  each  of  the  12  pc.  Immediately  following 
these  numbers  is  recorded  the  total  number  of  yards  in  the  12  pc.  The 
total  number  of  yards  should  be  found  by  horizontal  addition. 

5.    MANUFACTURER'S 

The  following  is  a  bill  for  neckwear.  The  different  styles  are  distin- 
guished by  the  marks  at  the  left  of  the  quantity.  This  form  is  common 
among  manufacturers,  jobbers,  and  wholesalers.  Bills  on  which  trade 
discounts  (see  page  242)  are  allowed  are  arranged  as  shown  in  this  bill. 


BILLS   AND   ACCOUNTS 


163 


Betogorlt,        Oct.    10, 

Jttessrs.    J.    E.   Whiting   &  Co. 

Bos-ton,    Mass. 


19 


Cerms  Net  30  days 

721 

ji 

doz.  Neckwear      $4.50 

6 

75 

1026 

i 

2 

27.00 

13 

50 

1025 

12 

27.50 

41 

25 

1020 

3 

4 

9.00 

6 

75 

923 

21 

18.00 

45 

00 

1015 

1| 

24.00 

42 

00 

155 

25 

Less  2% 

3 

11 

152 

14 

6.    FURNITURE 

In  the  following  bill  the  goods  were  sold  delivered  on  the  cars  (f .  o.  b.) 
Boston,  but  the  shippers  prepaid  the  freight  to  Bangor.  The  freight  is  a  part  of 
the  selling  price  and  is  added  to  the  amount  of  the  bill,  as  shown  in  the  model. 


-'9- 


TERMS 


Bought  of  E.   M.   PRAY,  SONS  &  CO. 

Manufacturers  of  Fine  Furniture 


LL. 


'JJ 


164 


PRACTICAL    BUSINESS   ARITHMETIC 


7.   WHOLESALE  COAL 
F.  H.  OSBORN  &  CO. 

SHIPPERS  OF 

Anthracite,   Bituminous,  and  Gas  Coal 


Sold  to  122. 


Terms 


2.0*70  a  # 


The  above  is  a  form  of  bill  that  is  generally  used  for  wholesale  transactions 
in  coal.    It  shows  that  the  coal  has  been  paid  for,  and  is  called  a  receipted  bill. 

8.    RETAIL   COAL 


.10. 


uou^t  of  jT,  Jtt»  (Everett  &  Co* 


'-0-  2. 


BILLS   AND   ACCOUNTS 


165 


On  page  106  is  a  form  of  coal  bill  used  by  many  retailers.  The  foregoing 
bill  shows  another  form  sometimes  used  by  retailers.  The  numbers  at  the 
left  of  the  hyphen  are  the  gross  weights,  and  the  numbers  at  the  right  the 
tares  of  the  different  loads. 

9.    CHINA    AND   GLASSWARE 

^Boston,          NOV.   6,  /9 

THE  WENTWORTH  =  STRATTON   CO. 

Rochester,    N.Y. 


of  Qsgood,   Jrauer  <£- 


erms  60  da.    net;    2%   10   da. 


1 

Dinner  Set,  130  pieces;  viz.: 

1  doz.  Plates,  8  in. 

] 

88 

1  "          7  " 

i 

63 

1  '           6  '  ' 

1 

38 

1  '           7  "  (deep) 

1 

63 

1  '   Fruit  Saucers,  4  in. 

75 

1  *    Individual  Butters 

50 

1/12  doz.  Covered  Dishes,  8  in.     $12.00 

1 

00 

1/12      Casseroles,  8  in.          13.50 

1 

13 

1/4       Dishes,  8  in.              2.50 

63 

1/12             10  "               4.50 

38 

1/12             12  '                7.50 

63 

1/12             14  '               10.50 

88 

1/6       Bakers,  8  in.               4.50 

75 

1/12      Sauce  Boats                4.00 

33 

1/12      Pickles                  3.00 

25 

1/12   '  '   Bowls                      2.00 

17 

1/12      Sugars                     6.00 

50 

1/12      Creams                     2.79 

23 

1        Handled  Teas 

2 

00 

1/2         "    Coffees            2.33 

1 

17 

1/12      Pitchers                  6.00 

50 

1/12      Covered  Butters  and 

Drainers                   9.00 

75 

19 

07 

25 

more  Dinner  Sets  as  above           19.07 

476 

75 

495 

82~ 

Crates 

7 

50 

Carting 

2 

10 

505 

42 

The  above  form  is  common  in  the  china  and  glassware  business.  In  this 
case  a  charge  is  made  for  the  crates  used  in  packing  and  the  prices  do  not 
include  delivery.  The  cost  of  the  crate  and  the  cost  for  carting  are  there- 
fore made  a  part  of  the  bill. 


166  PRACTICAL   BUSINESS   ARITHMETIC 

10.    LUMBER 
3{.  ^M.  ZBickford  60. 

{Boston,  ^Mass.,  Oct.     8, 


Sold  to  L.  A.  Hammond  &  Co. 

Paterson,  N.J. 

Pgt  .    net   cash;     bal.    in  5   da.    less   ~L\ 


23, 

289 

ft. 

1    v    ol     n-i 
2    A    ^2    U-L 

N. 

C. 

Ceiling  $ 

(18.50 

$430 

.85 

3, 

520 

* 

"            2 

tt 

tt 

tt 

17.00 

59 

.84 

10, 

307 

tt 

3    v    ol        -i 
Q    /s    c/2       -1- 

tt 

tt 

tt 

13.50 

139 

.14 

1, 

690 

tt 

"            2 

it 

It 

tt 

12.50 

21 

.13 

$650 

.96 

Less 

freight 

(45 

,200  Ib.    at  24^) 

108 

.48 

$542 

.48 

Lumber  is  generally  sold  by  the  thousand  feet.  In  the  above  bill  the  goods 
were  sold  free  on  board  cars  (f.  o.  b.)  Paterson,  N.J.,  but  the  shippers  have 
not  prepaid  the  freight.  They  find  that  these  charges  are  $108.48  and  deduct 
this  amount  from  the  total  of  the  bill.  In  the  wholesale  lumber  business  the 
prices  quoted  usually  include  the  cost  of  delivery,  and  when  the  freight  charges 
are  not  known  at  the  time  of  making  the  shipment,  they  are  paid  by  the 
consignees  and  deducted  from  the  amount  of  the  bill  on  the  arrival  of  the 
goods.  The  freight  bill  is  then  sent  to  the  shippers  for  credit. 

WRITTEN   EXERCISE 

1.  Study   the   model   bill,  page  160.     Increase  the  price  of 
each  article  25^  and  then  copy  and  find  the  amount  of  the  bill. 

2.  Study  the  first  model  bill,  page  161,  and  then  copy  and  find 
the  amount  of  it  at  the  following  prices:  hams,  27^;   coffee, 
23^;  mustard,  31^;  cocoa,  39^. 

3.  Study  the  second  model  bill,  page  161,  and  then  copy  and 
find  the  amount  of  it  at  the  following  prices :  porcelain  knobs 
#8,  $1.121;  #16,81.25;  steelyards  #64,  811 ;  #17,18.331; 
jack-planes  #14,  |6;  #21,16.25;  #48,16.75. 


BILLS   AND   ACCOUNTS  167 

4.  Apr.  15,  you  bought  of  S.  S.  Pierce  Co.,  Boston,  Mass., 
for  cash:   25  gal.   finest  New  Orleans  molasses  at  48^;  15  gal. 
fancy  sugar-house   sirup    at  49/;   75  Ib.   raw  mixed  coffee  at 
29^;  25  Ib.  raw  Pan-American  coffee  at  19^;  5  cartons  Fowle's 
entire-wheat  flour  at  39|^;  £bbl.  Franklin  Mills  flour  at  $6.75; 
l  bbl.  pastry  flour  at  15.25.     Write  the  bill. 

5.  Mar.    19,   Frank   M.  Richmond  &  Co.,   New  York  City, 
sold  to  Charles  M.  Thompson,  Poughkeepsie,  N.Y.,  12  doz.  por- 
celain knobs:   3  doz.  #71  at  $6.35,  9  doz.  #74  at  16.75;  12 
doz.    shingle  hatchets:   6  doz.  #16  at  19.75,    6  doz.   #34  at 
$12.50;   7  doz.  steel  squares:  3  doz.  #91  at  $35,  4  doz.  #73 
at  $33.     Terms:  30  da.     Write  the  bill. 

6.  Study  the  model  bill  on  page  162.     Increase  the  prices 
of  the  articles  marked  124  and  132  five  cents  each  and  the  re- 
mainder of  the  articles  one  cent  each;  then  copy  and  find  the 
amount  of  the  bill. 

7.  Nov.   15,  J.  B.  Ford  &  Co.,  Albany,  N.Y.,  bought  of  the 
Clinton  Mills,  Little  Falls,  N.Y.,  10  pc.  percale  shirting  con- 
taining 42, 48,  521, 58,  62,  38, 49,  51,  54,  and  461  yd.,  at  71  f ;  10  pc. 
fine  wool  cheviot  containing  581,  42,  49,  51,  442,  46,  48,  412,  39, 
and  42  yd.,  at  $1.12|;   5  pc.  cashmere  containing  493,  401,  483, 
491,  and  49  yd.    at  $1.37-}.      Terms:    60  da.,  or  3%  discount 
for  cash  within  10  da.     Write  the  bill. 

8.  Study  the  first   model   bill   on  page  163.      Increase  the 
prices   of   styles    1026,    1025,    1020,    and    923,    25^   each   and 
diminish  the   prices   of   the  other  styles  25^  each;  then  copy 
and  find  the  amount  of  the  bill. 

9.  Sept,  24,  Geo.  W.   Fairchild,    Buffalo,  N.Y.,  bought  of 
E.  M.  Lawrence  &  Co.,  New  York  City,  silk  ribbon  as  follows  : 
12  pc.  #1142  at  $2.25;  5  pc.  #1321  at  $1.25;  25  pc.  #171 
at  $4.371;  8  pc.  #  1927  at  $1.75  ;   36  pc.  #2114  at  $1.66f ;  15 
pc.   #1371  at  $1.331;  15  pc.  #624  at  $4.371  ;  12  pc.  #909  at 
$1.871;  25  pc.  #1008  at  $3.331;  25  pc.  #1246  at  $4.75;   18 
pc.  #2119  at  $1.121.     Terms:  30  da.,  or  2%  discount  for  cash 
in  10  da.     Write  the  bill. 


168  PRACTICAL   BUSINESS   ARITHMETIC 

10.  Study  the  second  model  bill  on  page  163.      Increase  the 
price  of  the  articles  marked  65  and  396,  25^  each,  and  diminish 
the  price  of  the  other  articles  12^  each;   then  copy  and  find 
the  amount  of  the  bill.     Freight  added,  $  14.70. 

11.  July  20,  The  Hayden  Furniture  Co.,  Rochester,  N.Y., 
bought  of  John  H.  Pray  &  Son,  Boston,  Mass.,  25  #31  card 
tables  at  $11 ;   24  #94  china  closets  at  $27.50  ;   15  #16   dining 
sets  at  $85;   25  #3060  fancy  rockers  at  $9.25;  15  #35  music 
cabinets  at  $2.75 ;   25  #26  mahogany  office  chairs  at  $12.50; 
12  #89  oak  sideboards  at  $125.      Terms:  30  da.     The  prices 
are  free  on  board  Boston,  and  the  shipper  prepaid  the  freight, 
$34.50.     Write  the  bill. 

12.  Study  the  first  model  bill  on  page   164.     Increase  the 
price  of  the  stove  coal  25^  per  ton  and  the  price  of  each  of  the 
other  kinds  12|^  per  ton;  then  copy  and  find  the  amount  of 
the  bill.     Receipt  the  bill  for  F.  H.  Osborn  &  Co. 

13.  May  19,  C.  E.  Williams  &  Co.,  Cleveland,  O.,  bought  of 
Fairbanks  &  Co.,  Scranton,  Pa. :  3  car  loads  of  stove  coal  weigh- 
ing 20,500,  26,400,  and  25,600  lb.,  respectively,  at  $4.75  per  ton 
(2000  lb.);  1  car  load  grate  coal  weighing  21,900  lb.  at  $4.25  per 
ton;  1  car  load  cannel  coal  weighing   22,500  lb.  at  $7.75  per 
ton.    Terms:  30  da.,  or  3%  discount  for  cash  in  10  da.     Write 
the  bill. 

14.  Study  the  second  model  bill,  page  164,  then  copy  and 
find  the  amount  of  it  at  $6.25  per  ton  for  each  sale. 

15.  Copy  the  bill  in  problem  14  in  accordance  with  the  model 
shown  on  page  106.     Make  the  price  of  the  coal  $6.66f. 

16.  Study  the  model  bill  on  page  165.     Increase  each  price 
given  five  cents  and  then  copy  and  find  the  amount  of  the  bill. 
Cost  of  crates  used  in  packing,  $6.40 ;  carting,  $2.80. 

17.  July  15,  Henry  Nelson  &  Co.,  Portland,  Me.,  bought  of 
Jones,  Stratton  &  Co.,  New  York  City,  5  doz.  plates,  8  in.,  at 
$1.50;  35  doz.  plates,  7  in.,  at  $1.35;    15  doz.  plates,   6  in., 
at  $1.10;   10  doz.  plates,  5  in.,  at  90^;   65  do/,  handled  teas  at 
$1.85      Terms:    30  da.      Cost  of  crate  used  in   packing,    $2; 
cartage,  75^.     Write  the  bill. 


BILLS   AND   ACCOUNTS  169 

18.  June  25,  F.  E.  Winter  &  Co.,  Batavia,  N.Y.,  bought  of 
E.   M.  Page  &  Co.,  Chicago,  111.,  provisions  as  per  problems  3, 
4,  and  5,  page  40.     Terms :  note  at  60  da.     Write    the    bill, 
using  current  prices. 

Find  the  net  weight  of  each  quantity  as  explained  in  §§  60-62. 

19.  Jan.    1,  John  P.  Alven,  100  Vine  St.,  bought  of  E.  E. 
Gray  Co.,  Boston,  Mass.,  2  Ib.  cafS  c?es  invalides  at  38^;  2  gal. 
maple  sirup  at  $1.35;    1  pkg.   magic  yeast  at  5/;    5  cartons 
Fowle's  entire-wheat  flour  at  22^ ;  3  cartons  Franklin  Mills  flour 
at  23  j^;   16  Ib.  pastry  flour  at  3|^;   5  gal.  fancy  sugar-house 
sirup  at  5(1^;   5  gal.  dark  molasses  at  41^;   6^-  Ib.  red  frosting 
sugar  at  12^;   7£  Ib.  rock-candy  crystals  at  9|^;   3  Ib.  C.  &  B. 
coffee  extract  at  25^ ;  1  Ib.  postum  cereal  at  22^ ;  2  Ib.  Chance's 
bread  soda  at  10^;   3  Ib.  cream  tartar  at  40^;   11  Ib.  Pyle's  sal- 
eratus  at  8^;   50  Ib.  granulated  sugar  at  5|^;   10  Ib.  powdered 
sugar  at  5|^;   5  Ib.  cut-loaf  sugar  at  6|^;  5  gal.  finest  P.  R. 
molasses  at  59^;  5  gal.  finest  N.  O.  molasses  at  61^;   1^  doz. 
bottles  maple  sirup  at  §3.75.     Write  the  bill. 

20.  Study  the  model  bill  on  page  166.     Increase  each  price 
50^,  make  the  freight  charge  2£^  per  hundred   pounds,   and 
then  copy  and  find  the  net  amount  of  the  bill. 

21.  Nov.  1,  J.  B.  Bickwell  &  Co.,  Worcester,  Mass.,  bought 
of  the  Northern  Lumber  Co.,  St.  Johnsbury,  Vt.,  on  60  days' 
credit  :   3  M  extra  spruce  clapboards  at  $52.50;   25  M  lath  at 
$3.75;  1500  ft.  2"  choice  cypress  lumber  at  $65  per  M  ;  1200 
ft.  2"  spruce  at  $23  per  M;   750  ft.  rift  hard  pine  at  $65  per 
M;  less  freight,  $42.50.      Write  the  bill. 

22.  June    15,    Helen    M.    Stone,    Cambridge,    Mass.,    sends 
Frank  M.  Spaulding  a  bill  for  tuition  and  supplies  to  date  as 
follows:   tuition,  one  term,  $37.50;    music    lessons,    $9.75;  1 
Practical  Elements  of  Elocution,  $1.65  ;   1  Allen  &  Greenough's 
Ccesar,  $1.35;   1  Allen  &  Greenough's  Cicero,  $1.55;   1  Myer's 
General   History,    $1.65.      Write  the  bill  and  receipt   it   for 
Helen  M.  Stone. 


170 


PRACTICAL   BUSINESS    ARITHMETIC 


STATEMENTS 


POLIO 


account  u>ith 


/  rt 


/  V 


209.  A  statement  is  an  abstract  of  a  customer's  account,  show- 
ing under  proper  dates  the  details  and  totals  of  debits  and  credits 
and  the  balance  remaining  unpaid. 


FOLIO. 


account  utifA 


^^ 


/z 


£22. 


Z^ 


BILLS  AND  ACCOUNTS 


171 


The  first  model  on  the  preceding  page  is  a  statement  of  C.  B.  McMeni- 
men's  account  for  January.  It  shows  that  the  charges  aggregate  $997.10, 
the  credits  $671.40,  and  that  the  balance  remaining  unpaid  is  $325.70. 

The  second  model  on  the  preceding  page  is  a  statement  of  C.B.  McMeni- 
men's  account  for  January  and  February.  The  items  on  the  January  state- 
ment are  summarized  in  the  record  "To  account  rendered,  $325.70."  The 
first  item  on  the  March  statement  will  be  "  To  account  rendered,  $412.20." 

WRITTEN    EXERCISE 

1.  During  March,  F.  E.  Smith,  Buffalo,  N.Y.,  bought   mer- 
chandise of  The  Hayden  Furniture  Co.,  Rochester,  N.  Y.,  as  per 
bills  rendered:  namely,  Mar.   3,  1400.80;   Mar.  15,  1360.90; 
Mar.    20,    1200.70;     Mar.    26,   1260.90;    Mar.    28,   $  130.50. 
During  the  same  time  he  made  cash  payments  on  account  as  fol- 
lows :  Mar.    15,   1400.80;  Mar.    23,  1360.90.      On  Mar.    27 
he  also  returned  goods  for  credit  amounting  to  118.60.    Render 
a  statement  of  F.  E.  Smith's  account. 

2.  During  April  the  above  account  was  charged  for  merchan- 
dise as  follows:  Apr.  15,  1720.50;  Apr.    27,   1260.90.     The 
account  was  also  credited  for  cash  as  follows  :  Apr.  16,  $200.70  ; 
Apr.  28,  1100.00.     Render  the  April  statement. 

3.  Copy  and  find  the  balance  of  the  following  statement: 

Boston,  Mass.,  Feb.  1,  19 
MRS.  C.  M.  SHERMAN 

931  BEACON  ST.,  City 
In  account  with  SPENCER,  MEAD  &  Co. 


Jan. 

1 

Account  rendered 

13 

64 

3 

2  pr.  Gloves                                2.50 
3  yd.  Velvet                                3.75 
12   «    Black  Silk                         2.10 

12 

6  pr.  Hose                                      35  ^ 
2  Hats                                          9.00 

30iyd.  Muslin                                 12J^ 
Cr. 

5 
15 

2  pr.  Gloves                                2.50 
1  Hat                                           9.00 

172 


PRACTICAL   BUSINESS    ARITHMETIC 


PAY   ROLLS 


PAY    ROLL  For  the  week  ending_ 


/ff         190 


222 


/r 


/F2.0 


2-7%*- 


%f7f<?F9 


This  form  is  most  common  among  manufacturing  establishments,  but 
it  is  also  used  by  printers,  contractors,  and  builders. 

Checks  are  sometimes  used  in  paying'  off  employees,  but  most  large  con- 
cerns find  the  envelope  system  the  most  convenient  and  satisfactory.  To 
pay  off  employees  by  the  envelope  system  it  is  necessary  for  the  bookkeeper 
to  find  first  the  amount  of  money  required  and  then  the  bills  and  fractional 
currency  that  are  necessary  to  pay  each  employee.  The  amount  required  is 
the  total  of  the  pay  roll,  and  the  bills  and  fractional  currency  desired  may  be 
found  as  shown  in  the  following  illustration.  This  illustration,  called  a 
change  memorandum,  shows  the  method  of  finding  just  the  denominations 
wanted  for  the  pay  roll  at  the  top  of  the  page.  A  change  memorandum 
may  be  proved  correct  as  shown  in  the  pay-roll  memorandum  at  the  top  of 
page  173. 


B  1  1.  i.s 

Co:xs 

$20 

$n 

$5 

$2 

$1 

50  ^ 

2.^ 

i  -0 

&l 

11 

1 

1 

1 

1 

1 

2 

1 

1 

1 

1 

3 

1 

1 

1 

1 

4 

1 

1 

1 

1 

1 

3 

6 

1 

1 

1 

1 

1 

1 

6 

1 

1 

1 

1 

1 

1 

1 

2 

8 

l 

1 

1 

2 

9 

1 

2 

1 

1 

1 

4 

10 

i 

1 

1 

1 

1 

2 

2 

1 

4 

1 

5 

6 

6 

0 

5 

9 

BILLS   AND   ACCOUNTS 


173 


When  the  amount  of  the  pay  roll 
and  the  necessary  bills  and  frac- 
tional currency  have  been  deter- 
mined, a  check  payable  to  the  order 
of  Pay  Roll  is  written.  A  pay-roll 
memorandum  similar  to  the  accom- 
panying form  is  then  attached  to 
the  check  and  both  are  sent  to  the 
bank.  The  pay-roll  memorandum 
should  foot  the  same  as  the  pay-roll 
book,  and  is  therefore  a  check  upon 
the  correctness  of  the  change  memo- 
randum. 

In  a  large  pay  roll  the  adept 
bookkeeper  frequently  estimates  the 
kind  of  change  required.  This  is 
done  by  scanning  the  pay  roll  first 
to  find  the  number  of  pennies  re- 
quired, then  the  number  of  nickels, 
etc.  The  experienced  book-keeper  can  make  a  very  accurate  estimate, 

PAY  ROLL     For  the  week  ending     /faw  £, 


FIRST 

NATIONAL  BANK 

Westjield,  Mass. 

PAT-ROLL  MEMORANDUM 

NELSON  fcf  CO. 

require  the  following:     * 

Nickels 

J- 

2~r 

6> 

60 

Quarters     . 

......   j- 

/  Z-<r 

Halves 

£ 

J    00 

Dollars  .     . 

j~ 

J  0  0 

.     7 

c's 

2.0  00 

7 

70  00 

2. 

4-0  00, 
.  s 

^ 

Bills  and  silver  necessary 


Q04^tifa££&, 


/fit 


2.  /o  7  /6  J~  7   6   7 


WRITTEN    EXERCISE 

1.    Study  the  model  pay  roll,  page  172,  and  find  the  amount  of 


it  at  the  following  wages  per  hour :  #1, 18^;  #2,  21f  ^  #3, 
#4,  35^;  #5,  331^;  #6,  35*; '#7,  37^;  #8,  35*;  #9,  271*; 
18|*.     Make  a  change  memorandum. 


174 


PEACTICAL   BUSINESS   ARITHMETIC 


2.  Study  the  model  pay  roll  on  page  173,  and  then  find  the 
amount  of  it  at  the  following  wages  per  hour:  #1,  50^;  $2,  45^; 
#3,  88J*;  #4,35^;  #5,  27^;  #6,  37-^;  #7,  25t;  #8,  33J^;  #9, 
44|^;  #10,22f/;  #11,22}*;  #12,  14f*;  #18,121*;  #14,80*. 

3.  j^Jake  a  pay  roll  memorandum  from  problem  2. 

WRITTEN    REVIEW    EXERCISE 

l.    Find  the  amount  of  each  of  the  following  bills : 

New   Tork,  May  31,   /p 
AfEssRS.  GRAY,  SALISBURY  &  Co. 

Rochester,  N.Y. 

Bought  of  J.  E.  PAGE,  SONS  &  Co. 

Terms :  net,  60  da. ;  2  %  10  da. 


CASE 

Pi  EC  KS 

DESCRIPTION  OF  ARTICLES 

YDS. 

PRICE 

ITEMS 

AMOUNT 

#364 

10 

Velveteen 

42i   40    40    46    38i 

40    42     42    41     39 

25^ 

#359 

12 

Corduroy 

36    38i   392  42    412  392 

37     37    41     45    41    401 

60  1  ^ 

#371 

15 

Gray  Homespun 

39    38    35    42    41 

45    39    41     34    37 

41     40     41     38     423 

83*  f 

#360 

6 

Storm  Serge 

40     42i    43    42     39    42i 

44  ? 

#373 

24 

Fine  English  Serge 

42    38    42    42    402  42J 

40     39    40     41     401  43 

42    42     382  38    41     42 

43    44    41     40    371  37 

1.37^ 

#381 

24 

Groveland  Flannel 

32     40    39    42     41     45 

45    46    35    41     38    41 

37     42     43    40     37     42 

37    40    42    41     44    41 

334 

BILLS   AND   ACCOUNTS  175 

2.  Make  out  a  bill  for  the  following  order.  Bill  the  English 
breakfast  tea  at  41^;  Finest  oolong  tea  at  65^;  Young  Hyson 
tea  at  97|^;  Choice  Japan  tea  at  59^;  Orinda  kaughphy  at 
81.90;  raw  Java  coffee  at  30|^;  gluten  flour  at  30^  a  carton 
arid  17.75  per  barrel.  Assume  that  half  a  chest  of  tea  weighs 
75  lb.,  and  a  mat  of  coffee  70  Ib. 

E.  M.  BARBER  &  SON 

RETAIL  GROCERS 
Springfield,  Mass.,         Aug  .          13  ,          19 

S.  S.  Pierce  Company, 

Boston,  Mass. 

Gentlemen: 

Please  ship  us  via  B.  &  A.  R.R.,  the  follow- 
ing goods: 

3  hf.  cht.  English  Breakfast  Tea 

3  "    "   Finest  Oolong  Tea 

5  "    "   Young  Hyson  Tea 

25  lb.  Choice  Japan  Tea 

5  5-lb.  cans  Orinda  Kaughphy 

7  mats  Raw  Java  Coffee 

5  hf.  bbl.  Gluten  Flour 

25  5-lb.  ^  cartons  Gluten  Flour 

Respectfully  yours, 


3.  Boston,  Mass.,  Apr.  16,  E.  O.  Burrill,  Philadelphia,  Pa., 
bought;  of  Jones,  Talcott  &  Co.,  on  account,  30  da.,  25  Turk- 
ish rugs  41  x  7  at  110.25  ;  750  yd.  matting  at  55^  ;  225  yd.  lin- 
oleum at  271^;  25  Turkish  rugs  8J  x  12  at  121.75  ;  25  Persian 
rugs  6x9  at  $12.25;  12  Persian  rugs  7  x  11  at  116.25;  10  rolls, 
each  containing  150  yards,  Brussels  carpeting  at  §2.25  ;  275  yd. 
Moquette  carpeting  at  $1.75.  Find  the  amount  of  the  bill. 


176 


PRACTICAL   BUSINESS   ARITHMETIC 


4.  Fill  the  following  order  :  English  breakfast  tea,  47  f ; 
Formosa  oolong  tea,  62|^;  Japan  tea,  62£l;  Ceylon  Pekoe 
tea,  90f  £  70  Ib.  to  each  half -chest. 

THE  WESTERN  TELEGRAPH  COMPANY 

INCORPORATED 

21,000  OFFICES  IN  AMERICA  CABLE  SERVICE  TO  ALL  THE  WORLD 


Receiver's  No. 


Time  Filed 


Check 


SEND  the  following  message  subject  to  the  terms 
of  the  Copnpapy,  wfcich  are  herebjr^agreed  to 

.-*£        JL  LS; 

To_ 


t  190 


5.  Yon  sold    Shepard,  Farmer   &  Co.,  the    following:   5M 
extra  cedar  shingles  at  1 3. 50  ;  15  M  clear  cedar  shingles  at  1 3. 00  ; 
20  M  extra  spruce  clapboards  at  $ 45.00  ;  15  M  clear  spruce  clap- 
boards at  143.00;   1230  ft.  random  hemlock  boards  at  $13.00; 
2760  ft.  planed  spruce  boards  at  $19  00  ;  2090  ft.  rough  spruce 
boards  at  #16.50;  18M  spruce  lath  at  $3.25;  6493  ft,  1  x  4" 
rift  flooring  at  $26.00.     Write  the  bill. 

6.  Copy  and  complete  the  following  time  card  : 

Time  worked  by  C.  E.   Small,  for  the  week  ending  Aug.  13. 
Rate  per  hour,  29\tf.      Occupation,  Painter. 


No. 

HOURS  WORKED 

TOTAL 
HOURS 
FOR  EACH 
ACCOUNT 

AMOUNT 
FOR  PL-veil 
ACCOUNT 

Sat. 

Sun. 

Mon. 

Tucs. 

Wed. 

Thtir. 

Fri. 

501 

2f 

41 

724 

2| 

9^ 

1029 

44 

8  1 

476 

H 

2? 

910 

10| 

9| 

735 

H 

i 

CHECK 

BILLS   AND   ACCOUNTS 


177 


TIME    SLIP 

Friday,    4/26,    1906 


TIME  SLIP 

4/27,  1906 


1 

2 
3 

4 
5 
6 
7 
8 
9 

IN 

651 
645 
644 
700 
700 
640 
756 
759 
756 

OUT 

1159 
1159 
1159 
1159 
1159 
1159 
1159 
1159 
1159 

IN 

1256 
1257 
1232 
1257 
1259 
1259 
1259 
104 
1255 

OUT 

459 
459 
459 
459 
459 
459 
459 
506 
459 

Saturday, 

IN      OUT       IN      OUT 

1  753  1200  1258  459 

2  703  1204  1256  504 

3  753  1150  1256  504 

4  655  1159  1259  459 

5  655  1159  1259  459 

6  701  1159  1255  459 

7  654  1150  1259  459 

8  654  1158  1259  459 

9  654  1159  1254  503 

The  above  slips  show  an  actual  record  of  time  for  9  employees  for  2  da. 
in  a  large  printing  establishment.  These  records  are  made  by  a  large  me- 
chanical timekeeper  and  at  convenient  times  are  copied  in  the  pay-roll  book. 
Fractions  are  recorded  to  the  nearest  \  of  an  hour.  In  the  above  slips,  the 
time  each  employee  arrived  in  the  morning  is  recorded  in  the  first  column, 
the  time  each  went  away  at  noon  in  the  second,  the  time  each  returned 
at  noon  in  the  third,  and  the  time  each  went  away  in  the  afternoon  in  the 
fourth.  Thus,  #1  arrived  at  7:53,  Saturday,  went  away  at  12:00,  re- 
turned at  12  :  58  and  worked  until  4  :  59  ;  time,  8  hr. 

7.  Copy  the  following  pay  roll,  enter  the  time  for  Friday  and 
Saturday  (from  the  above  slips),  find  the  amount  of  the  pay  roll 
as  in  previous  exercises,  and  make  a  change  memorandum  and 
a  pay-roll  memorandum. 

PAY   KOLL         FOR  THE   WEEK   ENDING   APRIL  27,  1906 


No. 

NAME 

NUMKER  OF  HOURS' 

WORK  EACH  DAY 

TOTAL 

No.   OF 
HOURS 

WAGES 

PER 

HOUR 

TOTAL 
WAGES 

REMARKS 

M. 

T. 

W. 

T. 

F. 

8. 

1 

A.  B.  Comer 

9 

8 

9 

9 

55f? 

2 

W.  D.  Ball 

9 

9 

9 

°1 

44f? 

3 

A.  M.  Snow 

9 

8 

8 

81 

44£? 

4 

R.  O.  Mark 

8 

9 

9 

9 

331? 

5 

Miss  Mary  Cane 

9 

8* 

9 

9 

331? 

6 

Miss  Ellen  Kyle 

8 

»1 

9 

9 

35? 

7 

D.  M.  Garson 

9 

81 

8 

91 

35? 

8 

S.  D.  Lane 

0 

81 

8^ 

9 

25? 

9 

Miss  Cora  Knapp 

9 

9 

81 

8 



22|? 

178 


PRACTICAL   BUSINESS   ARITHMETIC 


EXPEESSAGE   AND   FREIGHTAGE 

WRITTEN  EXERCISE 

1.  I  wish  to  express  five  separate  packages  from  Boston, 
Mass.,  to  Cincinnati,  O.  The  rate  per  100  Ib.  is  quoted  at 
12.00.  If  the  packages  weigh  15  Ib.,  73  Ib.,  86  Ib.,  126  Ib., 
and  29  Ib.,  respectively,  what  will  be  the  express  charge? 

Small  packages  are  usually  sent  by  express.  The  charge  varies  with  the 
distance  and  is  stated  at  so  much  per  100  Ib.  The  following  table  shows 
the  rate  for  smaller  weights,  when  the  rate  per  hundred  pounds  is  $2.00, 
$2.50,  $3.00,  $3.50,  $4.00,  and  $4.50  : 

CHARGES  FOR  PACKAGES  WEIGHING  LESS  THAN  100  POUNDS 
WHEN  THE  RATE  Is: 


$2.00 

$2.50 

$3.00 

$3.50 

$4.00 

$4.50 

1  Ib.  $  .25 

1  Ib.  $  .25 

1  Ib.  $  .25 

1  Ib.  $  .25 

1  Ib.  $  .25 

1  Ib.  $  .30 

2      .35 

2     .35 

2     .35 

2     .35 

2     .35 

2      .35 

3     .45 

3     .45 

3      .45 

3     .45 

3     .45 

3      .45 

4      .50 

4     .55 

4      .60 

4     .60 

4      .60 

4      .60 

5      .55 

5     .60 

5     .«5 

5     .70 

5     .70 

5      .75 

7      .60 

7      70 

7     .75 

7     .80 

7     .85 

7      .90 

10      .70 

10     .75 

10     .80 

10     .90 

10     1.00 

10     1.00 

15      .75 

15     .85 

15     .90 

15     1.00 

15     1.10 

15     1.15 

20      .85 

20     1.00 

20     1.10 

20     1.20 

20     1.25 

20     1.30 

25     1.00 

25     1.10 

25     1.20 

25     1.30 

25     1.50 

25     1.50 

30     1.00 

30     1.15 

30     .30 

30     1.50 

30     1.60 

30     1.70 

35     1.00 

35     1.25 

35     .40 

35     1.60 

35     1.70 

35     1.90 

40     1.00 

40     1.25 

40      .50 

40     1.75 

40     1.85 

40     2.00 

45     1.00 

45     1.25 

45     .50 

45     1.75 

45     2.00 

45     2.25 

50     1.00 

50     1.25 

50     .50 

50     1.75 

50     2.00 

50     2.25 

Pound  rates  (2^,  2|^,  3^,  etc.)  are  charged  for  everything  over  50  1b. 
Weights  between  those  named  in  the  table  are  charged  at  the  rate  for  the 
next  higher  weight. 

2.  The  express  charge  from  Boston  to  Chicago  is  quoted  at 
$2.50  per  hundred  pounds.  Find  the  express  charges  on  four 
separate  packages,  weighing  47  Ib.,  16  Ib.,  12  Ib.,  and  15  Ib., 
respectively,  sent  from  Boston  to  Chicago. 


BILLS   AND   ACCOUNTS 


179 


3.  A  publisher  sent  a  package  of  books  by  express,  C.  O.  D., 
from  Boston  to  Detroit.    The  rate  is  quoted  at  12.00  per  100  Ib. 
If  the  books  are  worth  1 75  and  weigh  56  Ib.,  how  much  should 
the  express  company  collect,  expressage  included? 

4.  The  express  rate  from  Lake  View,  Mich.,  to  Boston  is 
quoted  at  $  3.00  per  100   Ib.      Find  the  amount   of   express 
to  pay  this  distance  on  10  pkg.,  weighing  12  Ib.,  10  Ib.,  9  Ib.,  21 
Ib.,  27  Ib.,  34  Ib.,  86  Ib.,  121  Ib.,  127  Ib.,  and  54  Ib.,  respectively. 

5.  If   the   express    rate   from  St.  Joseph,  Mo.,    to    Boston, 
Mass.,  is  quoted  at  14.50  per  100  Ib.,  which  is  the  cheaper  and 
how  much,  to   send  three   separate    2-lb.    packages  from    St. 
Joseph  to  Boston  by  mail  or  by  express? 

6.  The    express   rate  from  Boston  to  St.   Albans,    Mo.,    is 
quoted  at  $3.50  per  100  Ib.     Find  the  express  charges  on  17 
separate  parcels  of  merchandise  sent  from  Boston  to  St.  Albans, 
when  the  weights  are  as  follows  :   15  Ib.,  17  Ib.,  25  Ib.,  14  Ib.,  18 
Ib.,  35  Ib.,  72  Ib.,  37  Ib.,  42  Ib.,  64  Ib.,  92  Ib.,  121  Ib.,  146  Ib.,  5 
Ib.,  15  Ib.,  31  Ib.,  41  Ib. 

7.  Find  the  amount  of  the  following  freight  bill : 


Date  of  W.  3-UuM*9       W.  B.  No.  ^£?      Albany,  N.Y. 

To  THE  INTERSTATE  TRANSPORTATION  COMPANT,  Dr. 

For  Transportation  f 


No. 


Bulky  goods  are  generally  sent  by  freight.  The  articles  are  divided  into 
different  classes,  according  to  quantity  and  character,  and  are  subject  to 
different  rates.  All  railroads  follow  some  official  classification.  All  official 
classifications  divide  freight  into  six  different  classes. 


180 


PRACTICAL   BUSINESS   ARITHMETIC 


Such  freight  as  organs  and  pianos  in  cases,  furniture,  statuary,  etc.,  is 
generally  designated  as  first-class  matter.  Baled  hay,  iron,  etc.,  in  car  loads, 
is  generally  designated  as  fifth-class  matter.  Building  blocks,  brick,  etc.,  in 
car-load  lots,  is  generally  designated  as  sixth-class  matter.  First-class  rates 
are  the  highest  and  sixth-class  rates  are  the  lowest  charged. 

Between  most  points,  shipments  weighing  less  than  100  Ib.  are  charged 
as  100  Ib.,  irrespective  of  weight. 

BOSTON   &   ALBANY   RAILROAD 

LOCAL  FREIGHT  TARIFF  BETWEEN 

BOSTON,  MASS. 

AND 


KATE  PEE  100  LB. 

RATE  PER  100  LB. 

% 

STATIONS 

Classes 

s 

STATIONS 

Classes 

1 

2 

3 

4 

5 

6 

1 

3 

3 

4 

5 

6 

21 

So.  Framingham 

10? 

9? 

7? 

6? 

5? 

4? 

98 

Springfield  .    . 

21? 

18? 

15? 

13? 

11? 

11? 

3i> 

Westboro     .     . 

11? 

10? 

9? 

7? 

6? 

5? 

108 

Westfield    .    . 

22? 

20? 

16? 

14? 

13? 

11? 

44 

Worcester    .     . 

13? 

12? 

10? 

8? 

8? 

6? 

14(> 

Athol.    .    .    . 

29? 

25? 

21? 

15? 

14? 

13? 

(J2 

Webster  .     .     . 

17? 

15? 

13? 

11? 

10? 

9? 

ir>o 

Pittsfield     .    . 

29? 

25? 

21? 

15? 

14? 

13? 

8;; 

Palmer     .     .     . 

19? 

16? 

14? 

12? 

11? 

10? 

KYI 

Albany    .    .    . 

30? 

27? 

22? 

15? 

14? 

13? 

8.  Using  the  table,  find  the  amount  of  freight  to  charge  on 
27,500  Ib.  sixth-class  matter,  from  Boston  to  Pittsfield. 

9.  Using   the  above   table,   find  the  amount  of  freight  to 
charge  on  27,290  Ib.  sixth-class  matter  and  890  Ib.  first-class 
matter  from  Boston  to  Albany ;  to  Westfield. 

10.  Using   the   above    table,  find  the  amount  of  freight  to 
charge  on  14,790  Ib.  fifth-class  matter  and  2170  Ib.  second-class 
matter  from  Boston  to  Palmer ;  to  Worcester ;   to  Pittsfield ; 
to  Springfield. 

11.  Using  the   above    table,  find  the  amount  of  freight  to 
charge  on  75  Ib.  first-class  matter,  125  Ib.  second-class  matter, 
1250  Ib.  third-class  matter,  7290  Ib.  fourth-class  matter,  21,490 
Ib.    fifth-class  matter,   and   64,640  Ib.  sixth-class  matter  from 
Boston  to  South  Framingham  ;   to  Westboro ;   to  Webster ;   to 
Springfield  ;  to  Athol  ;  to  Albany. 


DENOMINATE   NUMBERS    , 
CHAPTER   XV 

DENOMINATE  QUANTITIES 
REVIEW   OF   THE   COMMON   TABLES1 

ORAL  EXERCISE 

1.  Which  of  the  following  numbers  are  concrete  ?  which  are 
abstract?  which  are  denominate? 

a.  16  /.  150  k.  36  min. 

b.  24  yr.  g.  21  yd.  I.  5  yd.  2  ft. 

c.  64  hr.  h.  65   A.  m.  3  yr.  4  mo. 

d.  12  men  i.  17  books  n.  10  T.  75  Ib. 

e.  15  desks  j.  34  houses  o.  5  A.  61  sq.  rd. 

2.  Define  an  abstract  number;  a   concrete    number;   a   de- 
nominate number;  a  simple  number ;   a  compound  number. 

3.  Which  of  the  numbers  in  question  1  are  simple  ?  which 
are  compound  ? 

ORAL   EXERCISE 

1.  Repeat  the  table  of  avoirdupois  weight. 

2.  Repeat  the   table    of   long    measure;   of   surveyors'   long 
measure;  of  square  measure  ;  of  surveyors'  square  measure. 

3.  Repeat  the  table  of  cubic  measure;   of  dry   measure;   of 
liquid  measure;   of  time  ;   of  angular  measure;  of  United  States 
money  ;  of  English  money. 

4.  Name   a   number  expressing  distance ;    two  numbers  ex- 
pressing area  ;  two  expressing  value  ;  three  expressing  capacity. 

5.  How  many  statute  miles  in  a  degree  of  the  earth's  sur- 
face   at   the    equator  ?    how   many   geographical    miles  ?   How 
many  feet  in  a  statute  mile  ?  how  many  inches  ? 

1  Tables  of  weights  and  measures  may  be  found  in  the  Appendix. 

181 


182  PRACTICAL   BUSINESS   ARITHMETIC 

REDUCTION 

ORAL   EXERCISE 

1.  Change  42  ft.  to  inches  ;  to  yards. 

2.  Express  15  yd.  as  feet  ;   as  inches. 

3.  Reduce  80  qt.  to  gallons  ;  to  pints. 

4.  Change  128  qt.  to  pecks  ;  to  bushels. 

5.  Express  120  pt.  as  quarts  ;  as  gallons. 

6.  What  part  of  a  yard  is  2  ft.?  £  ft.?  \  ft.? 

7.  Reduce  5  bu.  to  pecks  ;  to  quarts  ;  to  pints. 

REDUCTION   DESCENDING 
210.    Example.     Reduce  4  T.  75  Ib.  to  ounces. 

SOLUTION.     Since  1  T.  =  2000   Ib.,    4    T.  =  4  times         2000 
2000  Ib.  =  8000  Ib.;  and  with  the   75   Ib.   added  this  =  4 

8075  Ib.     Since  1  Ib.  =  16  oz.,  8075  Ib.  =  8075  times  16  oz. 


=  129,200  oz.,  the  required  result.  -,  p 

8075  times  16  oz.  =  16  times  8075  oz.;  therefore  8075    - 
times  16  oz.  is  found  as  shown  in  the  margin.  129200,  No.  of  OZ. 

WRITTEN    EXERCISE 

Reduce  : 

1.  115'  6"  to  inches.  5.  3J  rd.  to  feet. 

2.  12  bu.  4  qt.  to  pecks.  6.  1J  T.  to  ounces. 

3.  £  16  15s.  to  shillings.  7.  12  A.  to  square  feet. 

4.  211  rd.  3  ft.  to  inches.  8.  161  cd.  to  cubic  feet. 

ORAL   EXERCISE 

1.  How  many  pecks  in  |  bu.?  in  |  bu.? 

2.  Change  .25  A.  to  square  rods;  .375  A.;  75  A. 

3.  Reduce  J  gal.  to  pints.     Express  ^  rd.  as  inches;  as  yards. 

WRITTEN   EXERCISE 
Reduce  : 

1.  |  mi.  to  feet.  4.    |  yd.  to  inches. 

2.  .75  cd.  to  cubic  feet.  5.    .375  mi.  to  feet. 

3.  I*  £  A.  to  square  feet.  6.    -^  hr.  to  seconds. 


DENOMINATE   QUANTITIES  183 

REDycTioN  ASCENDING 

211.    Example.     Express  176  qt.  dry  measure  in  higher  de- 
nominations. 

SOLUTION.  Since  8  qt.  =  1  pk.,  divide  by  8  and  obtain  8)176  qt. 
as  a  result  22  pk.  Since  4  pk.  =  1  bu.,  divide  by  4  and  ob-  4)22  pk. 
tain  as  a  result  5  bu.  2  pk.  F~  TL  o  n^. 

WRITTEN   EXERCISE 

Reduce  to  higher  denominations  : 

1.  3840  ft.                    5.    816  pk.  9.  15,120" 

2.  1054  pt.                  6.    106,590  ft.  10.  51,200  cu.  ft. 

3.  14,400  sec.               7.   43,560  sq.  in.  11.  145,152  cu.  in. 

4.  2000  sq.  in.             8.    27,900  Ib.  avoir.  12.  27,900  oz.  avoir. 

ORAL   EXERCISE 

1.  Reduce  |  ft.  to  the  fraction  of  a  yard. 

2.  Change  .16  cwt.  to  the  decimal  of  a  ton. 

3.  What  part  of  a  yard  is  1  in.?  2  in.?  -|-  in.? 

4.  What  decimal  part  of  an  acre  is  16  rd.?  40  rd.? 

5.  What  part  of  35  bu.  is  7  bu.?  of  1J  bu.  is  |  bu.? 

WRITTEN   EXERCISE 

1.  Reduce  1J  in.  to  the  fraction  of  a  foot;  of  a  yard. 

2.  Reduce  10s.  9c?.  to  the  fraction  of  a  pound  sterling. 

SOLUTION.     The  successive  divisors  for  reducing  pence  to 
pounds  sterling  are  12  and  20  respectively.     Divide  9d.  by      1^)        yd. 
12  and  the  result  is  .75s.     Put  with  this  the  10s.  in  the  prob-      20)10.  75s. 
lem  and  the  result  is  10.75s.     Divide  10.75s.  by  20  and  the  £.5375 

result  is  £.5375.     Or 

10s.  9eZ.  =  129d.     £  1  =  240d.     Therefore  10s.  Qd.  =        =  £.5375. 


3.  Reduce  4  yd.  1|  ft.  to  the  decimal  of  a  rod. 

4.  Reduce  10s.  6d.  2  far.  to  the  decimal  of  a  pound  sterling. 

5.  Reduce  5  T.  721  Ib.  to  tons  and  decimal  of  a  ton  ;  6  T. 
1750  Ib.;  12  T.  290  Ib.;  29,240  Ib.;  28,390  Ib. 

6.  Find  the  cost  of  1750  Ib.  of  coal  at  16.25  per  ton;  of 
2170  Ib.;  of  690  Ib.;  of  1360  Ib.;  of  3240  Ib.;  of  32590  Ib. 


184  PEACTICAL   BUSINESS   ARITHMETIC 

ADDITION   AND   SUBTRACTION 

ORAL  EXERCISE 

State  the  sum  of: 

1.  2.  3.  4. 

12  ft.  1  in.            5  Ib.  8  oz.              15  rd.  5  ft.  10  mi.  8  rd. 

6        3  6        3  17 2_  8       40 

5.                                    6.                                 7.  8. 

5  rd.  2  ft.  11  ft.  2  in.  5  bu.  1  pk.  5  mi.  20  rd. 

82-i  8i  80  17         13 

7         2|  3        3  9         1  11         10 

State  the  difference  between : 

1.  2.  3.  4. 

90  mi.  300  rd.  75  rd.  12|  ft.  30  yd.  2  ft.  44  bu.  3  pk. 
75  120  26  4-|  17  1J  29 1_ 

5.  6.  7.  8. 

11  mo.  12  da.        12  mo.  31  da.        11  mo.  15  da.       98  gal.  2  qt. 
6  6  8          17  _2 9_          69 1__ 

212.    Examples,     l.    Three  jars  of  butter  weighed  48  Ib.  7  oz., 
45  Ib.  9  oz.,  and  53  Ib.  11  oz.     Find  the  total  weight. 

SOLUTION.     Arrange  the  numbers  as  in  simple  addition,         4011        7 

so  that  units  of  the  same  order  stand  in  the  same  vertical 

-to  v 

column.     'Adding  the  first  column  at  the  right,  the  result  is  ~  ^ 

27  oz.  =1  Ib.  11  oz.;  write  11  oz.  and  carry  1  Ib.      Adding         ^0          •* 

the  pounds,  the  sum  is  147.  147  Ib.  11  OZ. 

2.    From  a  barrel  containing  379  gal.  1  qt.   of  molasses,  17 
gal.  3  qt.  were  sold.      How  much  remained  unsold  ? 

SOLUTION.     Arrange  the  numbers  as  in  simple  subtraction,      gy  _,  j    -j  Q^ 
so  that  units  of  the  same  order  stand  in  the  same  vertical      ^7         '3 

column.      3  qt.   cannot  be  subtracted  from  1  qt.;    therefore      — — '- — 

mentally  take  1  gal.  (4  qt.)  from  37  gal.  and  add  it  to  1  qt.,  ^  £ai'  -  cl^i' 
making  5  qt.  5  qt.  —  3  qt.  =  2  qt.  Inasmuch  as  1  gal.  was  added  to  1  qt.,  there 
are  but  36  gal.  remaining  in  the  minuend  ;  36  gal.  —  17  gal.  =  19  gal. 


DENOMINATE   QUANTITIES  185 

WRITTEN   EXERCISE 


Find  the  sum  of : 


1. 

2. 

3. 

4. 

£140 

6s. 

£139 

5s. 

84 

T.  75  Ib. 

279 

T.  840  Ib. 

159 

3 

214 

5 

96 

14 

364 

210 

162 

4 

921 

3 

78 

79 

872 

220 

139 

2 

141 

7 

37 

41 

146 

140 

167 

4 

10 

9 

19 

63 

214 

180 

129 

3 

171 

8 

84 

79 

926 

230 

136 

4 

215 

7 

97 

13 

210 

420 

147 

2 

321 

5 

87 

125 

75 

750 

Find  the  difference  between  : 

5.  6.  7.  8. 

11  mo.  17  da.  11  mo.  1  da.  8  mo.  14  da.  9  mo.  17  da. 

8         31  9       31  2         29  2         31 

9.    From  a  pile  of  wood  containing  74|  cd.,  28  J  cd.  and  15 J 
cd.  were  sold.     How  much  remained  unsold? 

10.  I  owned  a  farm  of  340  A.  when  I  bought  an  adjoining 
field  of  741  A.     I  then  sold  140 f  A.     What  is  the  remainder 
of  the  farm  worth  at  §75  per  acre  ? 

11.  An  English  merchant  had  on  hand  Jan.  1  goods  valued 
at  £5927  10s.;    during  the  following  six  months  he  bought 
goods  at  a  cost  of  £4920  10s.  and  sold  goods  to  the  amount  of 
£  7926  4s.     If  the  value  of  the  goods  on  hand  July  1  of  the 
same  year  was  £4120  10s.,  what  has  been  the  gain  or  loss  in 
English  money  ?  in  United  States  money  ? 

FINDING  THE   DIFFERENCE  BETWEEN   DATES 

213.  In  the  foregoing  problems  in  addition  and  subtraction 
only  compound  numbers  of  two  denominations  were  used. 
These  are  practically  the  only  compound  numbers  met  with  in 
business,  if  the  case  of  finding  the  difference  between  two  dates 
is  excepted. 


186  PRACTICAL   BUSINESS   ARITHMETIC 

214.  The  difference  between  two  dates  may  be  found  by  com- 
pound subtraction,  or  by  counting  the  actual  number  of  days 
from  the  given  to  the  required  date. 

In  business  transactions  involving  long  periods  of  time,  the  difference  is 
generally  found  by  compound  subtraction  ;  but  in  transactions  involving 
short  periods  of  time,  the  difference  is  generally  found  by  counting  the 
exact  number  of  days. 

215.  Examples.     1.    A  mortgage  dated  Oct.  15,  1901,  was 
paid  Apr.  6,  1907.     How  long  had  it  run  ? 

SOLUTION.     Write  the  later  date  as  the  rninu-      1907  yr.     4  mo.     6  da. 
end  and  the  earlier  date  as  the  subtrahend.   April      1901  10  15 

being  the  4th  and  October  the  10th  month,  write  r r  01    j — 

4  and  10  respectively  instead  of  the  names  of  the 
months.     Consider  30  da.  a  month  and  12  mo.  a  year  and  subtract  as  usual. 

2.    Find  the  difference  between  Apr.  21  and  July  27. 

SOLUTION.    Write  the  number  of        9  fa^  jn  April 
days  remaining  in  April,  the  number      gj[  ja    in  May 
in   May  and  June,  and  finally  the      on  j       •      Tune 
number  in  July  up  to  and  including      ^  ^  jn  jujy 
July  27.     The  sum  of  these  numbers      — —   -  ; 

is  the  required  time  expressed  with      97  da-  f  rom  APnl  21  to  July  27 
exactness.     Observe  that  the  total  time  excludes  the  first  and  includes  the  last 
day  of  the  given  dates. 

ORAL   EXERCISE 

/State  the  exact  number  of  days  between : 

1.  Mar.  12  and  Apr.  16.  5.  July  1  and  Oct.  1. 

2.  Apr.  27  and  May  31.  6.  June  30  and  Sept.  1. 

3.  May  31  and  July  18.  7.  July  31  and  Nov.  7. 

4.  June  7  and  Aug.  16.  8.  Aug.  31  and  Dec.  1. 

WRITTEN   EXERCISE 

Find  the  exact  number  of  days  between : 

1.  Apr.  2  and  Nov.  25.  5.    Mar.  18  and  Nov.  27. 

2.  Mar.  1  and  Sept.  18.  6.    Mar.  17  and  July  28. 

3.  Mar.  15  and  Nov.  2.  7.    June  16  and  Sept,  18. 

4.  Apr.  21  and  Dec.  31.  8.    June  19  and  Nov.  29. 
9.    Find  the  difference  between  Jan.  3,  1907,  and.each  of  the 

following  dates:  May  15,  1904;  Sept.  6,   1905;  Apr.   8,   1901; 
Mar.  12,  1889.     Find  the  difference  by  compound  subtraction. 


DENOMINATE   QUANTITIES  187 

MULTIPLICATION    AND   DIVISION 

ORAL  EXERCISE 

Multiply:  Divide: 

1.  3  ft.  by  6.  7.    27  yd.  by  9. 

2.  1J  mi.  by  8.  8.    225  ft.  by  7J  ft. 

3.  9  Ib.  4  oz.  by  2.  9.   48  ft.  6  in.  by  2. 

4.  18  Ib.  1  oz.  by  9.  10.    540  yd.  by  18  yd. 

5.  IT  yd.  2  in.  by  9.  11.    164  Ib.  12  oz  by  4. 

6.  19  gal.  1  qt.  by  3.  12.    640  mi.  160  rd.  by  20. 
216.    Examples.     1.    How  much  hay  in  8  stacks  each  contain- 
ing 5  T.  760  Ib.  ? 

SOLUTION.     8  times  760  Ib.  =  6080  Ib.  =  3  T.  80  Ib.  ;         5  ^    -T^Q  ITU 
write  80  in  place  of  pounds  and  carry  3.     8  times  5  T.  = 
40  T.  ;  40  T.  -f  3  T.  carried  =  43  T.    The  required  result 


is  therefore  43  T.  80  Ib.  43  T.      80  Ib. 

2.  An   importer    paid  £  87  10s.  for   50  pc.  of   bric-a-brac. 
What  was  the  cost  per  piece  ? 

SOLUTION.     Since  50  pc.   cost  £87  10s.,  1  pc.  costs  £     1      |5s 

sV  of  £  87  10s.     £;  of  £  87  =  £  1  with  an  undivided  re-  r/^  ^  S7  -  =po~ 
mainder  of  £  37  ;   write  £  1  in   the   quotient  and   add 

£  37  to  the  next  lower  denomination  ;  £  37  10s.  =  750s.  ^   of   750s.  =  15s. 

3.  At  10s.  .Qd.  per  yard,  how  many  yards  can  be  bought  for 
£  15  15s.  ? 

SOLUTION.     The  dividend  and 
divisor    are     concrete    numbers  ; 

therefore     reduce    them    to    the          £  15  15s.  =  3780t?. 
same  denomination  before  divid-          10s    Qd       =  126t? 


that  is  30  yd.  can  be  bought. 

ORAL   EXERCISE 

1.  At  72  $  per  gross  what  will  2  doz.  buttons  cost  ?  4  doz.  ? 
7  doz.  ? 

2.  How  many  3-oz.  packages  can  be  put  up  from  4  Ib.  of 
pepper  ? 

3.  Find  the  cost  of  3  T.  of  bran  at  30^  per  hundredweight; 
of  5  T.  at  50^  per  hundredweight. 


188  PRACTICAL   BUSINESS   ARITHMETIC 

4.  How  many  1-lb.  packages  can  be  put  up  from  15  T.  of 
breakfast  food  ? 

5.  When   coal  is  $  6  per  ton  what  will  7000  Ib.  cost  ?   6400 
lb.?  3600  Ib.  ? 

6.  Find  the  cost  of  2400  lb.  of  flour  at  $  2.25  per  hundred- 
weight; of  4400  lb.;  of  3200  lb. 

7.  At  12  J  f  per  quire  what  will  480  sheets  of  paper  cost  ? 
240  sheets  ?  2880  sheets  ?  720  sheets  ? 

8.  I  buy  3  qt.  of  milk  per  day.     If  I  pay  5  4  per  quart, 
what  is  my  bill  for  July  and  August  ? 

9.  I  bought  3  gro.  pens  at  60  $  a  gross  and  sold  them  at  the 
rate  of  2  for  1  4  ;  what  was  my  gain  or  loss  ? 

10.  I  bought  3|  bu.  of  apples  at  $1.00  per  bu.  and   sold 
them  at  50  $  a  peck.     What  was  my  gain  ? 

11.  I  sold  4 \  cd.  of  wood  for  $  27  and  thereby  lost  $  9  on 
the  cost.     What  was  the  cost  per  cord  ? 

12.  A  dealer  bought  5  rm.  of  paper  at  $  1.25  per  ream  and 
retailed  it  at  20  f  a  quire.     What  was  his  gain  ? 

13.  At  14.80  per  ream  what  will  3  qr.   of  paper  cost?     At 
13.60  per  ream  what  will  1  qr.  cost?  7  qr.  ? 

14.  If  the  gross  weight  of  a  load  of  straw  is  3380  lb.  and  the 
tare  1580  lb.,  what  is  the  straw  worth  at  $4.00  per  ton  ? 

15.  A  dealer  bought  pens  at  60^  a  gross  and  retailed  them 
at  the  rate  of  6  for  5  j.     What  did  he  gain  on  1  gro.?  on  6 
gro.?  on  8  gro.? 

WRITTEN  EXERCISE 

1.  Find  the  cost  of  10  pwt.  7  gr.  of  old  gold  at  $'1.25  per 
pennyweight;   of  12  pwt.  4  gr.  at  $1.10  per  pennyweight. 

2.  I  bought  3J  A.  of  city  land  at  $125  an  acre  and  sold  it 
at  50  f  per  square  foot.     Did  I  gain  or  lose  and  how  much  ? 

3.  Give  the  length  of  a  double-track  railroad  that  can  be 
laid  with  352,000  rails  30  ft.  long. 

4.  I  bought  a  barrel  of  cranberries  containing  2J  bu.  at  $4 
per  bushel  and  retailed  them  at  15^  a  quart.     Did  I  gain  or 
lose  and  how  much  ? 


DENOMINATE   QUANTITIES 


189 


5.  From  a  farm  of  375  A.  I  sold  25f  A.     What  is  the  re- 
mainder worth  at  $125  per  acre  ? 

6.  Find  the  cost  (a)  in  English  money  and  (5)  in  United 
States  money  of  360  doz.  cotton  hose  at  5s.  2d. 

SOLUTION,     (a)  5s.  2d.  =  5Js.      360  times  5$*.  =  1860s.  =  £  93,  the  cost  in 

English  money. 

(6)  £1=$4.8665.       93  times  $4.8665  =  $452.58,  the  cost  in 
United  States  money. 

7.  Copy  and  find  the  amount  of  the  following   invoice  : 


Terms. 


Bought  of  E.  M.  LLOYD  &  SON 


5/2,  4/3,  and  12/-  in  the  price  column  =  5s.  2rf.,  4s.  3rf.,  and  12s., 
respectively. 

8.  The  distance  around  a  square  garden  is  48  rd.   12  ft. 
Find  the  length  of  one  side  of  it. 

9.  Reduce  12500  to  English  money. 

SOLUTION.  £1  =  $4. 8665.  #2500 -s- 4.8665  =  51.372.  61.372  x  £1  =  £51.372. 
.372  x  20s.  =  7.44s.  .44  x  I2d.  =  5.28d.  .28  x  4  far.=  1.12  far.  Hence  $ 2500  = 
£51. 7s.  5d.  1  far. 

10.  Find  the  value  in  United  States  money  of  a  post-office 
money  order  for  <£5  18s.  6c?.;  for  £3  12s. 

11.  Change  $100  to  English  money  ;  1 135  ;  |  250  ;  $  1250. 

12.  A  coal  dealer  bought  448  T.  of  coal  by  the  long  ton  at 
14  per  ton  and  sold  it  by  the  short  ton  at  $5.25  per  ton.     Did 
he  gain  or  lose  and  how  much  ? 


190 


PRACTICAL   BUSINESS  ARITHMETIC 


13.  A  druggist  bought  by  avoirdupois  weight  5  Ib.  of  pep- 
permint oil  at  $2.501  per  pound  and  retailed  it  at  50^  an 
ounce,  apothecaries'  weight.  What  was  his  gain  ? 

217.  Farm  products  which  are  handled  in  bulk  are  frequently 
bought  and  sold  by  the  bushel.  The  statutory  weights  of  the 
bushel  for  some  of  the  common  commodities  are  shown  in  the 
following  table : 

STATUTORY  WEIGHTS  OF  THE  BUSHEL 


COMMODITIES 

WEIGHT  IN 
AVOIRDUPOIS 
POUNDS 

EXCEPTIONS 

Barley 

48 

Ala.,  Ga.,  Ky.,  and  Penn.,  47;  Ariz.,  45;  Cal.,  50. 

Beans 

60 

N.  H.  and  Vt.,  62. 

Clover  Seed 

60 

Corn,  Shelled 

56 

Ariz.,  54;  Cal.  52. 

Oats 

32 

Me.,  N.J.,  Va.,30;  Md.,26. 

Potatoes,  Irish 

60 

Md.,  Penn.,  and  Va.,  56. 

Rye 

56 

Cal.,  54. 

Wheat 

60 

218.     Example.     What  will  4260  Ib.  of  wheat   cost  at  80  1 
per  bushel? 

SOLUTION.    In  examples  of  this   character   the          71 
principles  of  cancellation  may  be  applied  to  advan- 
tage. 

In  problems  1-4  in  the  following  exercise  the  price  is  per  bushel  in  each  case. 


X  80  ff  __  &  r  g  OQ 


WRITTEN 

1.  Find  the  total  value  of : 
6640  Ib.  wheat  at  84  £ 

4230  Ib.  wheat  at  95  £ 

2.  Find  the  total  value  of : 
3264  Ib.  oats  at  25  £ 

2400  Ib.  oats  at  48^. 
2560  Ib.  oats  at  37}  £ 

3.  Find  the  total  value  of : 
3660  Ib.  clover  seed  at  $4.50. 
1200  Ib.  clover  seed  at  14.75. 
2472  Ib.  clover  seed  at  $4.20. 


EXERCISE 


1260  Ib.  wheat  at  90  £ 
6120  Ib.  wheat  at  87}  £ 


6951  Ib.  oats  at  32^. 
1920  Ib.  oats  at  33}  £ 
3840  Ib.  oats  at  29  j£ 

5040  Ib.  shelled  corn  at  47}  t. 
2800  Ib.  shelled  corn  at 
2240  Ib.  shelled  corn  at 


DENOMINATE   QUANTITIES  191 

4.  Find  the  total  value  of  : 

3793  Ib.  rye  at  11.12.  6160  Ib.  rye  at  90^. 

9240  Ib.  rye  at  $1.25.  3080  Ib.  rye  at  97J£ 

6720  Ib.  rye  at  $1.121  7924  Ib.  rye  at  $1.12. 

5.  The  gross  weights  and  the  tares  of  ten  loads  of  wheat 
were  4260  -  1260,     4310  -  1260,     3890  -  1260,     4160  -  1260, 
3860-1260,   4180-1260,   4370-1260,   4290-1260,   4370- 
1260,4480-1260  Ib.,  respectively.      Find  the    value   of   the 
wheat  at  $1.121  per  bushel. 

ORAL  REVIEW  EXERCISE 

1.  Find  the  cost  of  2500  Ib.  of  hay  at  $12  per  ton. 

2.  What  is  a  ton  of  wheat  worth  at  90^  per  bushel  ? 

3.  Change  4860  Ib.  to  tons  ;  3640  Ib.;  4280  Ib.;  6240  Ib. 

4.  Change  2.5  T.  to  pounds;  .75  T.;  2.03  T.;  11.004  T. 

5.  Change  6  mi.  to  rods ;   50  rd.  to  feet ;   330  ft.  to  rods. 

6.  How  much  more  than  1  ton  does  70  bu.  of  oats  weigh  ? 

WRITTEN  REVIEW  EXERCISE 

1.  Find  the  total  cost  of  : 

3260  Ib.  at  $5.25  per  ton.  4960  Ib.  at  $8.00  per  ton. 

3840  Ib.  at  $7.50  per  ton.  5800  Ib.  at  $6.25  per  ton. 

4560  Ib.  at  $6.871  per  ton.  5200  Ib.  at  $5.25  per  ton. 

2.  Find  the  total  cost  of  : 

3500  lath  at  $3  per  M.  1500  brick  at  $8  per  M. 

3600  Ib.  hay  at  $9  per  ton.  4260  Ib.  coal  at  $4  per  ton. 

3150  Ib.  pork  at  $4.50  per  cwt.        60  Ib.  beef  at  $4.75  per  cwt. 

3.  Find  the  total  value  of  : 

COMMODITY  GROSS  WEIGHT  TARE  PRICE 

A  load  of  coal  6460  Ib.  2140  Ib.  $6.25  per  T. 

A  load  of  straw  3680  Ib.  1680  Ib.  $3.25  per  T. 

A  load  of  wheat  4160  Ib.  1620  Ib.  851^  per  bu. 

A  load  of  oats  4760  Ib.  1560  Ib.  311^  per  bu. 

A  load  of  coal  4230  Ib.  1530  Ib.  $7.25  per  T. 

A  load  of  paper  rags  3260  Ib.  1260  Ib.  \t  per  Ib. 

A  load  of  old  iron  3480  Ib.  1280  Ib.  \t  per  Ib. 

A  load  of  corn  meal  4160  Ib.  1620  Ib.  75^  per  cwt. 


192 


PRACTICAL   BUSINESS    ARITHMETIC 


4.  A  church  was  lighted  by  kerosene  lamps  and  the  amount  of 
oil    consumed    each   evening   was   1J  qt.     If   the  church  was 
lighted  2  evenings  each  week  for  1  yr.,  what  was  the  cost  of 
the  oil  at  14^  per  gallon  ? 

5.  An  American  lady  shopping  in  Paris  bought  10yd.  of 
lace  at  20  francs  per  yard ;   6  pr.   of  gloves  at  10  francs  per 
pair.    What  was  the  amount  of  the  bill  in  United  States  money? 

6.  A  local  dealer  bought  448  T.   of  coal,  by  the  long  ton, 
at  $5.50  per  ton  and  sold  it  by  the  short  ton  at  §6.     If  the 
waste  and  loss  amounted   to  2  short  tons,  how  much  did  he 
gain? 

7.  Without  copying,  find  the  amount  of  the  following  in- 
voice : 


Leith,  Scotland,. 


/ 
INVOICE    OF  HOSIERY 


/Q 


Num- 
ber 


Quantity 


Article  and  Description 


Price 


Extension 


CM 


J 


8.  Find,  by  compound  subtraction,  the  difference  between 
Sept.  14,  1908,  and  each  of  the  following  dates:  Jan.  8,  1881; 
Feb.  7, 1883;  Mar.  9, 1890;  Apr.  27, 1895;  May  20, 1897;  June 
17,1899;  July  25, 1900;  Aug.  15,  1901;  Sept.  24,1903;  Oct. 
19,  1904;  Nov.  18,  1905;  Dec.  15,  1906. 


CHAPTER   XVI 


PRACTICAL    MEASUREMENTS 
DISTANCES   AND   SURFACES 

DISTANCES 

219.    An  angle  is  the  divergence  of  two  lines  from  a  common 
point. 

Thus  the  divergence  of  the  lines  BA  and  EC  from 


the  point  B  is  the  angle  ABC. 

220.    A  right  angle  is  the  angle  formed  when  one  straight  line 
so  meets  another  as  to  make  the  two  adjacent 
angles  equal.     The  lines  forming  the  angles  are 
perpendicular  to  each  other.  c- 


Thus  the  two  angles  ABC  and  ABD  are  right  angles,  and  the  lines  AB 
and  CD  are  perpendicular  to  each  other. 

221.  An  acute  angle  is  less  than  a  right  angle  ;  an  obtuse 
A  angle  is  greater  than  a  right  angle. 

^X^  _  Thus  the  angle  ABC  is  an  acute  angle,  and  the  angle 

ABD  is  an  obtuse  angle. 

222.  A  surface  is  that  which 
has   length  and  width,  but  not 
measurable  thickness.     A  level 
surface,  as  the  surface  of  still 
water,  is  called  a  plane  surface 
or  a  plane. 

223.  A  rectangle  is  a  plane  figure  bounded  by  four  straight 

lines  and  having  four  right  angles. 

A  square  is  a  rectangle  whose  sides 
are  all  equal. 

193 


194 


PRACTICAL   BUSINESS   ARITHMETIC 


224.  A  triangle  is  a  plane  figure  bounded  by  three  straight 
lines  and  having  three  angles. 

A  triangle  is  called  equilateral  when  all  its  sides  are  equal ; 
isosceles  when  any  two  of  its  sides  are  equal ;  scalene  when  no 
two  of  its  sides  are  equal. 

225.  A  right  angled  triangle  is  a   triangle  having   a  right 
angle. 

A  triangle  containing  an  acute  angle  is  sometimes  called  an 
acute-angled  triangle ;  a  triangle  containing  an  obtuse  angle,  an 
obtuse-angled  triangle. 


226.  The  perimeter  of  a  plane  figure  is  the  distance  around  it. 

227.  A  circle  is  a  plane  figure  bounded 
by  a  regularly  curved  line,  every  point  of 
which  is  equally  distant  from  a  point  within 
called  the  center.     The  circumference  of  a 
circle  is  the  curved  line  which  bounds  it ; 
the  diameter  is  any  straight  line  passing 
through  the  center  and  terminating  in  the 
circumference ;  the  radius  is  one  half  the 

diameter.     An  arc  is  any  part  of  the  circumference  of  a  circle. 


ORAL    EXERCISE 

1.  Measure  very  accurately  the   diameter  and  the  circum- 
ference of  each  of  several  circular  objects,  such  as  an  ink-well 
cover,  a  coin,  a  ring,  a  plate,  or  a  wheel.     Record  the  measure- 
ments in  each  case. 

2.  Divide  each  circumference  by  its  diameter,  carrying  the 
result  to  four  decimal  places. 

3.  Find  the  average  of  the  several  quotients. 

4.  How  many  times  the  diameter  of  a  circle  is  its  circum- 
ference ? 

5.  A  piece  of  circular  stove  pipe  7  in.  in  diameter  is  ap- 
proximately   22   in.    in  circumference ;    the    circumference   is 
approximately  how  many  times  its  diameter  ?     If  the  diameter 
of  a  circle  is  21  in.,  what  is  its  circumference  ? 


PRACTICAL   MEASUREMENTS 


195 


228.  It  is  proved  in  geometry  that  the  circumference  of  a 
circle  is  3.1416  times  the  diameter. 

229.  Therefore,  to  find  the  circumference  of  a  circle  when 
the  diameter  is  given,  multiply  the  diameter  by  3.1416. 

230.  And,  conversely,  to  find  the  diameter  of  a  circle  when 
the  circumference  is  given,  divide  the  circumference  by  3.1416. 


WRITTEN   EXERCISE 

1.  Draw    neat   figures  to  represent  each  of  the  following: 
rectangle,  triangle,  square,  circle,  right-angled  triangle,  equi- 
lateral triangle,  isosceles  triangle,  scalene  triangle,  radius  of  a 
circle,  arc  of  a  circle. 

2.  A  parlor  is  18  ft.    6  in.   long  and  12  ft.    3    in.   wide. 
What  will  be  the  cost,  at  28  j*  per  foot,  of  a  molding  extend- 
ing around  the  room  ? 

3.  The  circumference  of    a   circle  is  113.0976  ft.     What  is 
the  length  of  the  longest  straight  line  that  can  be  drawn  across 
the  circle?     Find  the  circumference 

of  a  circle  whose  radius  is  21  ft. 

4.  What  will  be  the  cost,  at  75^ 
per  yard,  of  carpeting  a  stairway  of 
18  steps,  the  tread  of  each  stair  being 
12  in.  and  the  riser  8  in.  ? 

5.  How     many    telegraph     poles, 

10  rd.  apart,  will  be  required  for  150  mi.  of  railroad? 

6.  Find  the  cost,  at  75^  per  rod,  of  fencing  the  fields  illus- 
trated in  the  accompanying  triangles: 

7.  A  rectangular  field 
is  100  rd.  long  and  60  rd. 
wide.     How  many  posts 
set  1  rd.  apart  will  be  re- 
quired to  inclose  the  field 
and  to  divide  it  into  four 

equal  fields?  ~  66 ft. 


196 


PRACTICAL   BUSINESS   ARITHMETIC 


AREAS 
ORAL  EXERCISE 

1.  What  is  the  area  of  a  square  1  rd.  on  each  side  ? 

2.  How  many  squares  1  rd.  on  each  side  in  a 
rectangle  6  rd.  long  and  1  rd.  wide  ? 

3.  How      many      rectangles, 
each  6  rd.   by  1  rd.,  in  a  rec- 
tangle 6  rd.  by  3  rd.  ? 

4.  How    many    square    rods 
in  the  area  of  a  rectangle  6  rd. 
long  and  3  rd.  wide  ? 

5.  How    many    square    rods 
in  the  area  of  a  rectangle  16  rd. 
long  and  132  ft.  wide  ? 

SOLUTION.  132  ft.  =  8  rd.  A  rectangle 
1  rd.  on  a  side  contains  1  sq.  rd.  But  the 
given  rectangle  is  16  times  1  rd.  long  and 


6rd. 

132  ft.  =  8  rd. 
8  x  16  sq.  rd.  =  128  sq.  rd. 
8  times  1  rd.  wide.    Therefore  the  required  area  is  16  x  8  x  1  sq.  rd.  or  128  sq.  rd. 

231.    In  the  foregoing  exercise  it  is  clear  that  the  product  of 
the  length  and  width  of  a  rectangle  equals  the  area. 

ORAL   EXERCISE 

Find  the  areas  of  rectangles  having  the  following  dimensions. 
Make  use  of  the  short  method  explained  in  §§  180-182. 


1.  6J-  ft.  by  6J  ft. 

2.  7J  rd.  by  7J  rd. 

3.  6.5  rd.  by  6.5  rd. 

232.  The  dimensions  of  a 
triangle  are  called  the  base  and 
the  altitude.  The  base  is  the 
side  on  which  the  triangle  ap- 
pears to  stand  ;  the  altitude  is 
the  perpendicular  distance 
from  the  base  to  the  highest 
point  of  the  triangle. 


4.  9.5  rd.  by  9.5  rd. 

5.  12.5  ft.  by  4.5  ft. 

6.  14.5  rd.  by  6.5  rd. 


Base 


PRACTICAL   MEASUREMENTS 


197 


ORAL  EXERCISE 

1.    How  does  the  area  of  the  triangle  on  the  right  compare 
with  the  area  of  a  rectangle  8  ft.  by  4  ft.  ? 

2.  Compare  the  area  of  the  triangle  on  the  left  with 
the  area  of  a  rectangle  12  rd.  by  5|  rd. 

3.  What  is  the  area  of  a  triangle 
whose  base  is  8  ft.  and  whose  alti- 

tude  is  9J  ft.? 

4.  The  area  of  a  triangle  equals  what  part  of  the 
area  of  a  rectangle  having  the  same  base  and  altitude? 

233.  In  the  above  exercise  it  is  clear  that  one  half  the  prod- 
uct of  the  base  and  altitude  of  a  triangle  equals  the  area. 

ORAL  EXERCISE 

State    the    areas   of  triangles   whose    bases  and   altitudes,    re- 
spectively, are  as  follows: 

1.  20  ft.,  18  ft.  3.    12  ft.,  41  ft. 

2.  12  ft.,  16  ft.  4.    19J  ft.,  8  ft. 

234.  If  a  circle  be  divided  as  in  the  figure  on  the  left  and  the 
parts  rearranged  as  in  the  figure  on  the  right,  it  will  be  clear 


that  the  area  of  the  circle  equals  the  area  of  the  twelve  tri- 
angles. The  altitude  of  each  triangle  is  the  radius  of  the  circle, 
and  the  sum  of  the  bases,  the  circumference. 

235.  It  is  therefore  clear  that  one  half  the  product  of  the 
circumference  and  radius  of  a  circle  equals  the  area. 

When  a  circle  is  divided  as  in  the  above  figure,  the  parts  are  not  exact  tri- 
angles ;  but  it  is  proved  in  geometry  that  the  area  of  a  circle  is  the  same  as 
that  of  a  triangle  having  a  base  equal  to  the  circumference  and  an  altitude 
equal  to  the  radius. 


198  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL    EXERCISE 

1.  The  base  of  a  triangle  is  8  in.  and  the  height  11  in.    What 
is  the  area  ? 

2.  A  field  contains  1280  sq.  rd.     If  the  width  is  32  rd.,  what 
is  the  length  ?          x 

3.  A  man  sold  a  lot  10  rd.  long  and  8  rd.  wide  at  the  rate  of 
1260  per  acre.     How  much  did  he  receive  ? 

4.  A  porch  is  20  ft.  long  and  6  ft.  wide.     How  many  square 
feet  of  oilcloth  will  be  required  to  cover  it  ? 

5.  A  canvas  on  which  a  portrait  is  painted  contains  1440  sq. 
in.     If  the  width  is  3  ft.,  what  is  the  length  ? 

WRITTEN    EXERCISE 

1.  A  circular  pavilion  has  a  radius  of  56|-  ft.     What  is  the 
area  of  the  floor  space  ? 

2.  A  city  lot  contains  ^  A.     If  it  is  200  ft.  long,  what  is  its 
width,  and  what  is  its  value  at  50  ^  per  square  foot  ? 

3.  The  floor  of  a  restaurant  50  ft.  long  and  40  ft.  wide  is 
covered  with  tiles  8  in.  square.     How  many  tiles  will  be  required? 

4.  A  small  park,    50  rd.  long  and  40  rd.  wide,   has  a  walk 
inclosing  it.     If  the  walk  is  1  yd.  wide,  how  many  square  feet 
does  it  contain  ? 

5.  How  many  square  feet  of  slate  will  be  required  to  furnish 
blackboard  surface  for  a  schoolroom  30  ft.  wide  and  42  ft.  long,  if 
the  slate  is  1  yd.  wide 

and  extends  across  one 
end  of  the  room  and 
one  third  the  length 
on  each  side  ? 

6.  The  accompany- 
ing    diagram     repre- 
sents a  field  of  wheat. 

It  is  drawn  on  a  scale  of  ^  in.  to  the  rod.     How  much  will  it 
cost,  at  50  ^  per  rod,  to  build  a  fence  around  the  field  ? 


PRACTICAL   MEASUREMENTS 


199 


Jin. 


iin. 


lin. 


7.  If  the  field  in  problem  6  yields  an  average  of  16^  bu.  of 
wheat  to  the  acre,  for  a  certain  season, 

what  is  the  crop  worth  at  10.95  per 
bushel  ? 

8.  The  accompanying   diagram  rep-  a 
resents  a  field  of  corn.     It  is  drawn  on 

a  scale  of  -£%  in.  to  the  rod.  If  the  field 
yields  an  average  of  28  bu.  to  the  acre 
for  a  certain  year,  what  is  the  crop  worth  at  55  f  per  bushel  ? 

PUBLIC   LANDS 

236.  In  the  more  recently  settled  parts  of  the  United  States, 
public  lands  are  surveyed  by  select- 
ing a  north  and  south  line  as  a  prin- 
cipal meridian  and  an  east  and  west 
line  intersecting  this  as  a  base  line. 
Other  lines  are  then  run,  at  intervals 
of  6  miles,  both  east  and  west  of  the 
principal  meridian,  and  north  and 
south  of  the  base  line.  These  lines  divide  the  land  into  tracts 
6  mi.  square,  called  townships.  The  lines  of  townships  running 
north  and  south  are  called  ranges. 

Thus  A  in  the  above  diagram  may  be  described  as  Tp.  1  N.,  R.  3  W.  ;  that  is, 
the  first  township  north  of  the  base  line,  in  the  third  range  west  of  the  principal 
meridian. 


237.    Each  township  is  divided  into  36  tracts,  each  1  mile 
square,  called  sections.     The  numbering  of  sections  in  every 
township  is  as  shown  in  the  dia- 
gram at  the  left. 

Sections  are  divided  into  halves 
and     quarters;     quarter     sections 
are    subdivided    into    halves    and 
-quarters. 

If  diagram  3  is  B  of  diagram  2,  and  diagram  2  is  A  of  diagram  1,  C  of  dia- 
gram 3  may  be  described  as  the  S.E.  J  of  S.E.  J,  Sec.  19,  Tp.  1  N.,  R.  3  W. 


200  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  chains  in  a  mile  ?  how  many  rods  ?  how  many 
feet  ?     How  many  rods  in  a  chain  ?  how  many  feet? 

2.  How  many  acres  in  a  field  50  ch.  by  40  ch.?  in   a   field 
40  ch.  square  ?  in  a  field  80  ch.  by  80  ch.  ? 

3.  A  field  has  an  area  of  4  A.     If  it  is  10  ch.  long,  how  wide 
is  it  and  what  will  it  cost  to  fence  it  at  50^  per  rod  ?  at  60^? 

WRITTEN    EXERCISE 

1.  Make  a  diagram  of  a  township  and  locate  N.  J,  Sec.  20. 

2.  Draw  a  diagram  illustrating  principal  meridian,  base  line, 
range  line,  and  township  lines,  and  mark  Tp.  2  S.,  R.  2  E.  and 
Tp.  1  N.,  R.  3  W. 

3.  Find  the  value,  at  112.50  per  acre,  of  Tp.  2  N.,  R.  3  W. 

4.  Find  the  cost  at  $25  per  acre  of  N.E.  £  of  N.W.  J,  Sec. 
20,  Tp.  1  N.,  R.  4  W. 

SQUAIIE  ROOT  AND  ITS  APPLICATIONS 
ORAL  EXERCISE 

1.  What  is  meant  by  factor?   by  exponent?   by  power  of  a 
number  ? 

2.  State  the  second  power  of  each  of  the  following  numbers  : 
1,  2,  3,  4,  5,  6,  7,  8,  9.     How  much  is  122,  132,  142,  152,  162? 

3.  Name  one  of  the  two  equal  factors  of  each  of  the  following 
numbers :  2,  4,  9,  16,  25,  36,  49,  64,  81,  100,  121,  144,  169,  196. 

238.    The  square  of  a  number  is  the  product  arising  from 
the  number  twice  as  a  factor.    The  square  root  of  a  number 
wo  equal  factors  of  the  number, 
quare  root  of  a  number  may  be  indicated  by  writ- 
er under  the   radical  sign  ^/~  or  by  placing  the 
)ve  and  to  the  right  of  the  number, 
r  196*  indicates  the  square  root  of  196. 

oquare  root  of  a  number  is  readily  derived  from  the 

process  by  which  the  square  is  formed. 


PRACTICAL   MEASUREMENTS  201 

241.  Example.     What  is  the  square  of  42? 

SOLUTION.     Since  42  =  40  +  2,  the  square  of  42  may  be  found  as  follows  : 

40  +  2 

40  +  2  402  =  1600 

(40x2)+22  2(40x2)=    160 

4Q2  +  (4Q  x  2) 2    =        4 

402+2(40  x2)  +  22  =  1764 

242.  In  the  preceding  process  it  is  shown  that  the  square  of 
a  number  is  equal  to  the  square  of  the  tens  plus  twice  the  product 
of  the  tens  by  the  unify  plus  the  square  of  the  units. 

243.  I2  =  1,  102  =  100,  1002  =  10000,  and  so  on ;   92  =  81,  992  = 
9801,  9992  =  998001,  and  so  on.     It  is  therefore  evident  that  the 
square  of  an  integral  number  contains  twice  as  many  figures  or 
one  less  than  twice  as  many  figures  as  the  number.     Hence,  if 
an   integral   number  be   separated  into  groups  of  two  figures 
each,  from  right  to  left,  there  will  be  as  many  figures  in  the 
square  root  as  there  are  groups  of  figures  in  the  number. 

244.  Examples.   1.    What  is  the  square  root  of  529  ? 

SOLUTION.     Beginning  at  the  right,  separate  the  number  into  5   29(23 

periods  of  two  figures  each.     The  greatest  square  in  5  is  4  and  ^ 

the  square  root  of  4  is  2,  the  tens'  figure  of  the  root.  Find  the 
remainder,  affix  the  second  period,  and  the  result  is  129.  This 
remainder  is  equal  to  twice  the  product  of  the  tens  by  the  units,  1  29 

plus  the  square  of  the  units  (§  242).  Twice  2  tens  is  4  tens  (40) 
and  4  tens  (40)  is  contained  in  129,  3  times ;  hence,  3  is  the  units'  figure  of  the 
root.  Twice  the  tens  multiplied  by  the  units  plus  the  square  of  the  units  is  the 
same  as  twice  the  tens  plus  the  units  multiplied  by  the  units.  Therefore,  annex 
3  units  to  the  4  tens  and  multiply  by  3  ;  the  result  is  129.  The  square  root  of 
529  is  thus  shown  to  be  23. 

2.    What  is  the  square  root  of  (a)  13.3225 ;   (5)  of  .0961  ? 

13  .32  25(3.65  .09  61(.31 

9  .09 


6.6)4  .32  .61). 00  61 

3  .96  .00  61 

7.25)     .36  25 
.36  25 


202  PRACTICAL   BUSINESS   ARITHMETIC 

245.  The  process  of  finding  the  square  root  of  a  number  may 
be  summarized  as  follows : 

Beginning  at  the  units,  separate  the  number  into  groups  of  two 
figures  each. 

Find  the  greatest  square  in  the  left-hand  group  and  write  its 
root  for  the  first  figure  of  the  required  root. 

Subtract  the  square  of  the  root  figure  from  the  left-hand  period 
and  annex  the  second  period  for  a  dividend. 

Take  twice  the  root  figure  already  found,  considered  as  tens, 
and  divide  the  dividend  by  it. 

Annex  the  quotient  to  both  the  root  and  the  trial  divisor  and 
multiply  by  the  units. 

Continue  in  like  manner  until  all  the  periods  have  been  used. 
The  result  will  be  the  square  root. 

If  a  number  contains  a  decimal,  begin  at  the  decimal  point  and  indicate 
groups  to  the  left  for  the  integral  part  of  the  root,  and  to  the  right  for  the 
decimal  part  of  the  root.  If  the  last  period  on  the  right  of  the  decimal 
point  has  but  one  figure,  annex  a  decimal  cipher,  as  each  decimal  period 
must  contain  two  figures. 

To  find  the  square  root  of  a  common  fraction,  extract  the  square  root  of 
the  numerator  and  denominator  separately.  If  the  terms  of  the  fraction 
are  not  perfect  squares,  reduce  the  fraction  to  a  decimal  and  then  extract 
the  square  root. 

WRITTEN  EXERCISE 

Find  the  square  root  of: 

1.  324.              5.   576.  9.  9025.  13.   f|. 

2.  484.              6.   1024.  10.  3364.  14. 

3.  676.              7.   7225.  11.  70.56.  is. 

4.  729.              8.   3969.  12.  150.0625.  16. 


246.  It  has  been  seen  that  the  area  of  a  square  is  the  product 
of  its  two  equal  sides.     It  therefore  follows  that  the  square  root 
of  the  area  of  a  square  equals. one  of  its  sides. 

247.  The  hypotenuse  is  the  side  opposite  the  right  angle  in  a 
right  triangle. 


PRACTICAL   MEASUREMENTS 


203 


248.  In  the  accompanying  illustration  it  will  be  seen  that  the 
square  on  the  hypotenuse  is  equal  to 

the  sum   of  the  squares  on  the  other 
sides.     Hence, 

249.  To  find  the  hypotenuse  take  the 
square  root  of  the  sum  of  the  squares  of 
the  base  and  altitude;  and 

250.  To  find  the  base  or  the  altitude 
take  the  square  root  of  the  difference  be- 
tween  the  squares  of  the  hypotenuse  and 
the  other  side. 

WRITTEN  EXERCISE 

1.  A  square  field  contains  5.625  A.     What  is  the  length  of 
one  of  its  sides  ? 

2.  Find  the  side  of  a  square  containing  the  same  area  as  a 
field  160  rd.  long  by  90  rd.  wide. 

3.  What  is  the  hypotenuse  of  a  right-angled  triangle  the  base 
of  which  is  30  ft.  and  the  altitude  40  ft.  ? 

4.  The  accompanying  diagram  represents 
a  piece  of  land.    It  is  drawn  on  the  scale  of 
-fa  in.  to  the  rod.     The  land  is  divided  into 
two  fields  by  the  line  AB.     Find  the  cost, 
at  50  f  per  rod,  of  fencing  the  two  fields. 

5.  What  will  be  the  cost,  at  $1.75  per  chain,  of  fencing  a 
square  field  containing  1.6  A.? 

ROOFING 

251.  Roofing  is  usually  measured  by  the  square  of  100  sq.  ft. 

252.  The  size  of  slates  used  for  roofing  varies  from  6  in.  by 
12  in.  to  16  in.  by  24  in. 

Contractors  and  builders  generally  use  prepared  tables  for  estimating  the 
amount  of  slate  to  be  used.  The  number  of  slates  per  square  varies  with 
the  size  of  the  slate.  Thus,  slates  16  in.  by  24  in.  require  86  per  square ; 
slates  6  in.  by  12  in.  require  533  per  square ;  etc. 


204 


PKACTICAL   BUSINESS  ARITHMETIC 


253.  All  shingles  average  4  in.  in  width  and  are  put  up  in 
bundles  of  250.     The  shingles  most  commonly  used  are  16  in. 
or  18  in.  long.     16-inch  shingles  are  generally  laid  4J  in.  and 
18-inch  shingles  5J  in.  to  the  weather. 

254.  A  shingle  4  in.  wide  laid  4J  in.  to  the  weather  will  cover 
18  sq.  in.     A  square  contains  14,400  sq.  in.     14,000  sq.  in.  -*- 
18  sq.  in.  =  800.     It  is  therefore  clear  that  800  16-inch  shingles 
will  cover  a  square  of  roof. 

255.  A  shingle  4  in.  wide  laid  5J  in.  to  the  weather  will  cover 
22  sq.  in.     14,400  sq.  in.  -T-  22  sq.  in.  =  655.     It  is  therefore 
clear  that  655  18-inch  shingles  will  cover  a  square  of  roof. 

In  practice  655  per  square  is  called  700  per  square. 


40  ft 


One  fourth  Pitch 


40ft. 


One  half  Pitch 


\ 


ORAL   EXERCISE 

1.  How  many  bundles  in  1000  shingles?  in  7500  shingles? 
in  26,000  shingles  ? 

2.  What  will   be   the  cost,   at  $4  per 
square,  of  tinning  a  roof  20  ft.  by  15  ft.  ? 

3.  A  certain  roof  requires  7610  shingles. 
How  many  bundles  of  shingles  must  be 
bought  to  cover  it  ? 

A  dealer  will  not  sell  a  fractional  part  of  a 
bundle  of  shingles. 

4.  How  many  slates  at  300  to  the  square 
will  be  required  for  a  flat  roof  30  ft.  by 
20  ft.  ? 

256.  The  rise  in   the  rafters  for  each 
foot  in  the  base  of  the  gable  is  called  the 
pitch  of  the  roof. 

257.  When  the  rise  of  the  roof  is  6  in. 
per  foot,  the  roof  is  said  to  have  one-fourth 
pitch. 

258.  When  the  rise  of  the  rafters  is  12  in.  per  foot,  the  roof 
is  said  to  have  one-half  pitch. 


40ft, 


Gothic  Pitch 


PRACTICAL   MEASUREMENTS  205 

259.  When  the  rise  of  the  rafters  is  15  in.  per  foot,  the  roof 
is  said  to  have  five-eighths,  or  Gothic  pitch. 

When  the  rise  of  the  rafters  is  6  in.  per  foot,  the  perpendicular  height  of 
the  gable  is  1  of  the  width  of  the  building ;  when  the  rise  is  12  in.  per  foot, 
the  height  of  the  gable  is  i  the  width  of  the  building;  when  the  rise  is  15 
in.  per  foot,  the  height  of  the  gable  is  f  of  the  width,  or  li  times  |  the  width 
of  the  building.  Hence  the  names  one-fourth  pitch,  one-half  pitch,  etc. 

ORAL    EXERCISE 

Find  the  height  of  the  gable  : 
WIDTH  OF  BUILDING      PITCH  OF  ROOF      WIDTH  OF  BUILDING      PITCH  OF  ROOF 

1.  30  ft.  £  3.    24  ft.  Gothic 

2.  50  ft.         12  in.  per  ft.          4.    36  ft.  J 

WRITTEN  EXERCISE 

1.  The  accompanying  diagram  represents  the  roof  of  a  shed 
16  ft.  wide.     If  the  ridge- 
pole is  68  ft.,  the  pitch  of 

the  roof  one  half,  and  the 
projection  of  the  rafters 
18  in.,  how  many  shingles 
16  in.  long,  laid  4J  in.  to 
the,  weather,  will  be  re- 
quired to  cover  the  roof  ? 

SOLUTION 

1  of  16  ft.  =  8  ft.  =  the  base  of  the  triangle  ABC. 

The  pitch  of  the  roof  is  £  ;  $  of  16  ft.  =  8  ft.  =  the  altitude  of  the  triangle  ABC. 

82  +  82  =  128  ;  128*  ='11.31,  number  of  feet  in  the  hypothenuse  of  ABC. 
18  in.  =  1.5  ft.  ;  11.31  ft.  +  1.5  ft.  =  12.81  ft.  =  the  length  of  the  rafters  or 
the  width  of  each  side  of  the  roof. 

2  x  68  x  12.81  ft.  =  1742.16  sq.  ft.  =  the  entire  surface  of  the  roof. 
1742.16  sq.  ft.  =  17.4216  squares;  17.4216  x  800  shingles  =  13937  shingles. 
As  bundles  of  shingles  are  not  broken  it  will  be  necessary  to  buy  14000  shingles. 

2.  A  building  is  40  ft.  wide.     If  the  length  of  the  ridge- 
pole is  80  ft.  and  the  projection  of  the  rafters  20  in.,  how  many 
shingles  18  in.  long  and  laid  5J  in.  to   the  weather  will  be 
required  for  the  roof,  the  pitch  being  J  ? 


206  PEACTICAL   BUSINESS    ARITHMETIC 

3.  A  building  is  30  ft.  wide.  If  the  length  of  the  ridge- 
pole is  60  ft.  and  the  projection  of  the  rafters  15  in.,  how  many 
shingles  16  in.  long  and  laid  4^  in.  to  the  weather  will  be 
required  for  the  roof,  the  pitch  being  ^? 

PLASTERING 

260.  Plastering  is  usually  measured  by  the  square  yard. 

261.  There  is  no  uniform  rule  with  respect  to  the  allowance 
to  be  made  for  doors,  windows,  and  other  openings. 

What  allowance,  if  any,  shall  be  made  for  openings  is  usually  stated  in 
the  contract  covering  the  work.  In  some  sections  it  is  customary  to  make 
allowance  for  one  half  the  area  of  the  openings ;  in  others,  for  the  full  area 
of  the  openings  ;  in  still  others,  for  a  stated  number  of  square  feet. 

In  giving  the  dimensions  of  a  room  carpenters,  architects,  and  mechanics 
write  the  length  first,  then  the  width,  and  finally  the  height.  They  also 
usually  write  5"  for  5  in.,  5'  for  5  ft.,  and  5'  x  5'  for  5  ft.  by  5  ft. 

ORAL   EXERCISE 

1.  What  is  the  perimeter  of  a  square  room  20'  on  a  side  ? 

2.  What  is  the  perimeter  of  a  dining  room  18'  x  12'  x  9'? 

3.  How  many  square  feet  in  the  four  walls  of  the  room  in 
problem  2,  not  allowing  for  openings  ?     in  the  ceiling  ?     in  the 
four  walls  and  the  ceiling  ? 

4.  How  many  square  yards  in  the  four  walls  of  a  room  24'  x 
16',  not  allowing  for  openings  ? 

5.  At  25^  per  square  yard,  what  will  it  cost  to  plaster  945 
sq.  ft.  ?     1080  sq.  ft.  ?     1440  sq.  ft.  ? 

WRITTEN   EXERCISE 

1.  What  will  it  cost,  at  27  ^  per  square  yard,  to  plaster  the 
walls  and  ceiling  of  a  hall  60'  x  40'  x  24',  making  an  allow- 
ance of   40  sq.  yd.  for  openings  ? 

2.  Find  the  cost,  at  26^  per  square  yard,  of  plastering  the 
walls  and  ceiling  of  a  room  18'  x  16'  6"  x  8'  6",  making  full 
allowance  for  2  doors  each  7'  6"  x  4'    3  windows  6'  x  4'. 


PRACTICAL   MEASUREMENTS 


207 


3.  What  will  be  the  cost  of  plastering,  with  hard  finish,  at 
34  $  per  square  yard,  the  walls  of  the  rooms  in  the  following 
dwelling  ? 

First  Floor.  Parlor,  14'  x  12'  ;  sitting  room,  12'  x  12'  ; 
dining  room,  12'  x  10'  ;  kitchen,  12'  x  10' ;  pantry,  8'  x  6'. 
All  rooms  on  this  floor  are  uniformly  8'  6"  high. 

Second  floor.  Front  chamber,  14'  x  12'  ;  back  chamber, 
12'  x  12'  ;  middle  chamber,  10'  x  9'  ;  hall,  23'  x  4'.  All  rooms 
on  this  floor  are  uniformly  8'  high. 

Allowance  is  made  for  40  openings  of  17  sq.  ft.  each. 

PAINTING 

262.  Painting  is  usually  measured  by  the  square  yard. 

263.  It  is  customary  to  make  no  allowance  for  windows,  the 
painting  of  window  sills  and  sashes  being  considered  as  expen- 
sive as  the  painting  of  the  surface  area  of  the  entire  window. 

WRITTEN  EXERCISE 

1.  What  will  it  cost,  at  25^  per  square  yard,  to  paint  the 
walls  of  a  room  20'  x  16'  x  12',  no  allowance  being  made  for 
doors  or  windows  ? 

2.  At  6J^  per  square  yard,  what  will  it  cost  to  kalsomine  the 
walls  and  ceiling  of  a  room  24'  x  18'  x  12',  allowing  for  a  door 
9'  x  4',  2  windows  7'  x  4',  and  a  wainscot  3'  high  around  the 
regular  surface  of  the  room  ? 

3.  Find  the  cost,  at  24^  per  square  yard,  of  painting,  with  two 
coats,  the  outside  walls  of  a 

tobacco  barn  68'  x  20'  x  25' 
with  gables  extending  10' 
above  the  ends  of  the  walls. 

4.  What  will  be  the  cost, 
at  22^  per  square  yard,  of 
painting  the  outside  walls  of 

a  barn  100'  x  40'  x  20'  with  gables  extending  10'  above  the  walls  ? 
with  gables  extending  12^-'  above  the  walls  ? 


208  PRACTICAL   BUSINESS   ARITHMETIC 


FLOORING 

264.  Flooring  is  measured  by  the  square  or  by  the  thousand 
square  feet. 

Professional  floor  layers  charge  by  the  square,  the  price  being  from  75 ^  to 
$1.50  per  square.  Carpenters  usually  work  by  the  day  in  laying  floors. 

Spruce  flooring  is  4"  or  5j"  in  width;  hardwood  flooring  is  2'1  or  2^"  in 
width.  In  flooring  there  is  considerable  waste  in  forming  the  tongue  and 
the  groove  of  the  boards.  When  flooring  is  3"  or  more  in  width,  it  requires 
about  \\  sq.  ft.  of  material  for  every  square  foot  of  surface  to  be  covered; 
when  flooring  is  less  than  3"  in  width,  it  requires  1^  sq.  ft.  for  every  square 
foot  of  surface  to  be  covered. 

265.  Example.    How   many  feet  of   spruce  flooring   will  be 
required  for  a  room  32'  x  24'  ? 

SOLUTION.     32  x  24  =  768,  the  number  of  square  feet  to  be  covered. 

1^  X  768  sq.  ft.  =  960  sq.  ft.,  the  quantity  of  flooring  required. 

WRITTEN    EXERCISE 

1.  Find  the  cost  at  $45  per  thousand  square  feet  of  a  hard- 
wood floor  for  a  room  20'  x  16'. 

2.  A  pavilion  is  70'  x  50'.     If  the  flooring  is  of  spruce,  what 
will  be  the  cost  at  $  27  per  thousand  square  feet  ? 

3.  In  a  two-story  dwelling  the  floor  area  measures  35'6"  x  26'. 
The  first  floor  is  to  be  of  hardwood  and  the  second  floor  of  spruce. 
Find  the  quantity  of  flooring  needed. 

4.  What  will  be  the  cost  of  a  hardwood  floor  in  a  room 
30' x  28',  if  the  labor  and  incidentals  cost  $25.50,  the  lumber 
$30.50  per  M.,  and  60  sq.  ft.  are  allowed  for  waste  ? 

5.  Find  the  cost  of  laying  an  oak  floor  20'  x  15',  reckoning 
the  labor  and  incidentals  at  $9.50,  the  floor  boards  at  $83^  per 
thousand,  and  estimating  that  there  is  a  waste  of  40  sq.  ft. 

6.  The  floors  in  a  three-story  dwelling  are  each  55'  4"  x  33' 
10".     The   first   floor   is    to  be  of   hardwood   worth  $50   per 
thousand  square  feet  and  the  other  floors  of  spruce  worth  $27 
per  thousand  square  feet.     If  it  costs  $1.10  per  square  for 
labor,  what  will  be  the  total  cost  of  laying  the  three  floors  ? 


PRACTICAL   MEASUREMENTS 


209 


CARPETING 

266.  Carpet  is  sold  by  the  yard.      Such   floor  covering  as 
oilcloth  and  linoleum  are  frequently  sold  by  the  square  yard. 

267.  In  determining  the  number  of  yards  of  carpeting  re- 
quired for  a  room  it  is  necessary  to  know  whether  the  strips 
are  to  run  lengthwise  or  crosswise. 

Carpets  are  generally  laid  lengthwise  of  a  room  ;  but  when  the  matter  of 
expense  is  an  item,  it  is  sometimes  more  economical  to  lay  the  strips  cross- 
wise. 

When  the  length  of  the  strips  required  is  not  an  even  number  of  yards, 
there  is  usually  some  waste  in  matching  the  pattern.  Merchants  will  sell 
fractional  lengths  but  not  fractional  widths  of  carpeting.  It  is  therefore 
frequently  necessary  to  cut  off  or  turn  under  a  part  of  a  strip. 

ORAL  EXERCISE 

1.  How  many  yards  of  carpet,  1  yd.  wide,  must  be  purchased 
for  a  room  5  yd.  long  by  4  yd.  wide  ? 

2.  The  accompanying  diagram  represents  a 
room  drawn  on  the  scale  of  ^  of  an  inch  to 
the  foot.     Find  the  dimensions  of  the  room. 

3.  How  many  strips  of  carpet,  1  yd.  wide, 
laid  lengthwise  of. the  room,  will  be  required 

for  problem  2  ?   How  many  feet  in  each  strip  ?    How  many  yards 
of  carpet  will  be  required  for  the  room  ? 

4.  The  accompanying  diagram  represents  a  room  drawn  on 
the  scale  of  ^  in.  to  the  foot. 

How  many  strips  of  carpet, 
1  yd.  wide,  laid  lengthwise 
of  the  room,  will  be  required 
to  cover  it  ?  What  part  of 
a. strip  must  be  cut  off  or 
turned  under  in  this  case? 

5.  How  many  feet  in  each 
strip  in  problem  4  ?  If  there  is 

.  -  £t  UJ.. 

no  waste  in  matching  the  pat- 
tern, how  many  feet  of  carpet  will  be  required  ?  how  many  yards  ? 


210 


PRACTICAL   BUSINESS  ARITHMETIC 


6.  If  the  strips  in  problem  4  are  run  crosswise  of  the  room, 
how  many  will  be  required  ?  what  will  be  the  length  of  each 
strip  ?     If  the  strips  in  problem  4  are  laid  crosswise  of  the  room, 
it  is  found  that  there  will  be  a  waste  of  6  in.  per  strip  in  match- 
ing.   Under  these  conditions,  how  many  yards  will  be  required? 

7.  If  the  carpet  in  problem  4  is  laid  the  most  economical 
way,  what  will  it  cost  at  $  1.50  per  yard  ? 

268.  Example.  How  many  yards  of  carpet  f  yd.  wide  will 
be  required  for  a  parlor  floor  20'  x  16'  6",  if  the  strips  run 
lengthwise  and  there  is  a  waste  of  6  in.  on  each  strip  for 
matching  the  pattern  ? 

SOLUTION.     Since    the    strips  16' 6"  =  3-3'=  3-3  yd 

run  lengthwise  of  the  room,  the  6 

width  of  the  room  divided  by         ¥  Jd-  ^  !  >'d-  =  7i  or  8  stnPs 
the  width  of  the  carpet  equals  20'  +  6"  =  20J' 

the  number   of  strips  required.       g   x  20^'  =  164'  =  54|  yd. 
V  yd-  •*• 1  =  7£, tne  no-  of  strips  ; 

but  since  an  even  number  of  strips  must  be  purchased,  7£  strips  must  be  called  8 
strips.  The  length  of  the  room  is  20'  and  there  is  a  waste  of  6  in.  per  strip ; 
hence  20J'  of  carpet  must  be  purchased  for  each  strip.  8  times  20£'  =  164'  = 
54f  yd.,  the  required  result. 

WRITTEN  EXERCISE 

1.  How  many  yards  of  carpet- 
ing 1  yd.  wide  will  be  required  to 
cover  the  chamber  in  the  accom- 
panying floor  plan,  if  the  strips 
are  to  run  lengthwise  and  there  is 
no  waste  in  matching  the  pattern  ? 

2.  Find  the  number  of  yards  of 
carpet  required  to  cover  the  room 
in   problem  1   if   the    strips   run 
across  the  room  and   there   is  a 
waste  of  6  in.  per  strip  in  match- 
ing the  pattern. 

3.  If  the  chamber  is  carpeted  in 

the  most  economical  way,  what  will  be  the  cost  at  f  1.25  per  yard? 


PRACTICAL   MEASUREMENTS 


211 


4.  How  many  yards  of  carpet  f  yd.  wide  will  be  required 
for   the   parlor   in   the   foregoing  floor  plan?     The  strips  are 
to  run  lengthwise  and  there  is   no    waste   in   matching    the 
pattern. 

The  cheaper  grades  of  carpet  are  usually  1  yd.  wide.     The  expensive 
grades,  such  as  Brussels,  Wilton,  etc.,  are  |  yd.  wide. 

5.  How  many  yards  of  carpet  |  yd.  wide  will  be  required 
for  the  dining  room  in  the  foregoing  floor  plan  ?     The  strips 
are  to  run  lengthwise  and  there  is  a  waste  of  6  in.  per  strip 
in  matching  the  pattern. 

6.  A   rug   18'  x  24'    is  placed  cen- 
trally on  a  floor  24'  x  30'  and  filling  is 
used  to  cover  the   remainder   of   the 
room.     If  the  rug  cost  -$29.50  and  the 
filling  27 1  $  per  yard,  what  is  the  cost 
of  covering  the  floor  ? 

7.  The  five  chambers  in  the  accom- 
panying  diagram    are   to   be   covered 
with  carpet  1  yd.  wide,  that  can  be 
matched  without  waste.    The  strips  in 
each  room  are  to  run  in  the  direction 

requiring  the  smaller  number  of  yards.     At  85^  per  yard,  what 
will  it  cost  to  cover  the  five  floors  ? 


PAPERING 

269.  Wall  paper  is  usually  sold  in  double  rolls  18  in.  wide 
and  16  yd.  long. 

Single  rolls  18  in.  wide  and  8  yd.  long  are  sometimes  used,  but  it  is 
generally  found  more  economical  to  use  double  rolls.  These  dimensions 
vary  more  or  less. 

Allowances  for  openings,  such  as  doors  and  windows,  are  made  in 
different  ways  by  different  paper  hangers.  Some  make  a  uniform  allow- 
ance for  each  opening,  while  others  make  allowance  for  the  exact  measure- 
ments of  the  openings. 

Any  whole  number  of  rolls  left  over  after  papering  may  usually  be  re- 
turned to  the  dealer. 


212  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  What  will  the  border  for  a  room  15'  x  18'  cost  at 
per  yard? 

2.  18  in.  =  f  ft.     30  ft  -r-  f  ft.  =  30  ft.  x  f  ft.  =  20.    Divide 
21  ft.  by  18  in. 

3.  A  wall  is  15  ft.  long  and  9  ft.  high.     If  there  are  no 
openings,  how  many  strips  will  be  required  to  cover  it  ?     How 
many  full  strips  can  be  cut  from  each  double  roll  of  paper  ? 
What  part  of  a  strip  will  run  to  waste?     How  many  rolls  will 
be  required  for  the  wall  ? 

4.  Suppose  that  in  problem  2  there  is  a  door  3'  x  8'.     What 
is  the  length  of  the  regular  surface  of  the  wall  ?     Fractional 
strips   must  be   counted  as   full  strips.      Why  ?     How   many 
strips  of  paper  will  be  required  to  cover  the  regular  surface  of 
the  wall  ?      Will    dealers  sell  a  fractional  part  of    a  roll  of 
paper?     How  many  rolls,  then,  will  be  required  for  the  regular 
surface  of  the  walls? 

5.  There  is  a  small  surface  over  the  door  in  problem  5  that 
has  not  been  considered.     What  may  be  used  to  cover  this 
surface  ? 

270.  Obviously,  to  estimate  the  quantity  of  paper  required 
for  a  room: 

From  the  perimeter  of  the  room  subtract  the  width  of  the  open- 
ings. Find  |  of  this  remainder  and  the  result  will  be  the  number 
of  strips  required.  Divide  the  number  of  strips  required  by  the 
number  of  full  strips  that  can  be  cut  from  each  roll  of  paper  and 
the  result  is  the  required  number  of  rolls. 

By  this  method  the  ends  of  the  rolls  are  supposed  to  be  utilized  for  the 
surface  above  the  doors  and  above  and  below  the  windows  and  other  irregu- 
lar places. 

The  height  of  the  room,  in  papering,  will  be  understood  to  mean  the 
distance  from  the  baseboard  to  the  frieze. 

To  estimate  the  paper  required  for  a  ceiling,  take  f  of  the  width  of  the 
room  for  the  number  of  strips  required.  Divide  the  number  of  strips  re- 
quired by  the  number  of  full  strips  that  can  be  cut  from  each  roll  and  the 
result  is  the  number  of  rolls  of  paper  required. 


PRACTICAL   MEASUREMENTS  213 

271.  Example.     How   many   double    rolls  of  paper  will  be 
required  for  the  walls  and  ceiling  of  a  room  2V  x  18'  x  8',  al- 
lowing for  2  doors  and  3  windows,  each  3J  ft.  wide? 

SOLUTION 

(21'  +  18')  x  2  =  78',  the  perimeter  of  the  room. 

5  x  3|'  =  17^',  the  total  width  of  the  openings. 

78'  -  17i'  =  6Qi',  the  perimeter  of  the  regular  surface  of  the  walls. 

f  of  60£  =  40i,  the  number  of  strips  of  paper  necessary  for  the  regular  surface. 

48'  -=-  8'  =  6,  the  number  of  strips  in  each  roll. 

40i  strips  -+•  6  strips  =  6  if,  or  practically  7  rolls  of  paper  required  for  the  walls. 

|  of  18  =  12,  the  number  of  strips  required  for  the  ceiling. 

48'  -f-  21'  —  2|,  or  practically  2,  the  number  of  strips  in  each  roll. 

12  strips  -=-  2  strips  =6,  the  number  of  rolls  required  for  the  ceiling. 

6  rolls  +  7  rolls  =  13  rolls  required  for  the  walls  and  ceiling. 

WRITTEN   EXERCISE 

1.  The  rooms  in  the  floor  plan,  page  210,  are  9;  high.     What 
will  it  cost,  at  95^  a  roll,  to  paper  the  walls  and  ceiling  of  the 
parlor,  making  allowance  for  2  double  doors,  each  6'  wide,  1 
single  door  3J'  wide,  and  2  windows,  each  3|'  wide? 

2.  How  many  rolls  of  paper  will  be  required  for  the  walls 
and  ceiling  of  the  dining  room  in  the  floor  plan,  page  210,  al- 
lowing for  1  double  door  6'  wide,  1  single  door  3J'  wide,  and  2 
windows  each  3^'  wide  ? 

3.  At  43^  per  roll  how  much  will  it  cost  to  paper  the  walls 
and  ceiling  of  the  chamber  in  the  floor  plan,  page  210,  allowing 
for  2  windows,  each  3|-'  wide,   1  double  door  6'  wide,  and  1 
single  door  3^'  wide. 

SOLIDS 

RECTANGULAR  SOLIDS 

272.  A  solid  is  that  which  has  length,  width, 
and  thickness. 

273.  A  rectangular  solid  is  a  solid  bounded 
by  six  rectangular  surfaces. 

274.  A  cube  is  a  rectangular  solid  having  six  square  faces. 


214  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.    If  A  in  the  accompanying  series  of  diagrams  is  1  cu.  ft., 
how  many  cubic  feet  in  B  ?   in  C  ?   in  D  ? 


2.  How  many  cubic  feet  in  a  block  of  granite  6  ft.  long,  1  ft. 
wide,  and  1  ft.  high  ?  in  a  block  6  ft.  long,  3  ft.  wide,  and 
1  ft.  high  ?  in  a  block  6  ft.  long,  3  ft.  wide,  and  3  ft.  high  ? 

3.  Find  the  volume  of  a  rectangular  solid  6  ft.  by  4  ft.  by  2 
ft. ;  a  rectangle  10  ft.  by  9  ft.  by  9  ft. 

4.  A  cellar  is  40  ft.  square  and  6  ft.  deep.     How  many  cubic 
yards  of  earth  were  removed  in  excavating  it  ? 

SOLUTION.     A  cube  1  ft.  on      6  X  40  X  40  X  1  CU.  ft.  =  9600  CU.  ft. 
the  side  contains  1  cu.  ft.    The      96QO  ^  f ^  _,_  97  =  3526  cu>  y(J. 
given  cube  is  40  x  1  ft.  long, 

40  x  1  ft.  wide,  and  6  x  1  f t.  high.     Therefore,  it  contains  6  x  40  x  40  x  1  cu.  ft., 
or  9600  cu.  ft. ;  and  9600  cu.  ft.  =  355f  cu.  yd. ,  the  required  result. 

275.    Ill  the  foregoing  exercises  it  is  clear  that  the  product  of 
the  three  dimensions  of  a  solid  equals  the  volume  or  solid  contents. 

WRITTEN  EXERCISE 

1.  A  box  car  is  50  ft.  6  in.  long,  8  ft.  4  in.  wide,  and  3  yd. 
high.     What  is  its  volume  ? 

2.  A  piece  of  timber  is  60  ft.  long  and  18  in.  square.     How 
many  cubic  feet  does  it  contain  ? 

3.  A  village  constructs  a  reservoir  for  a  water  supply.     The 
length   is    100   yd.,  the  width  70  yd.,  and  the    depth    15    ft. 
What  will  be  the  cost,  at  23^  per  cubic  yard,  of  excavating  the 
reservoir  ? 


PRACTICAL   MEASUREMENTS 


215 


WOOD 

276.  Wood  is  measured  by  the  cord. 

277.  A  cord  of  wood  or  stone  is  a  pile  8  ft.  long,  4  ft.  wide, 
and  4  ft.   high.     It  con- 
tains 128  cu.  ft. 

The  word  "cord,"  as  prac- 
tically used  in  wood  measure, 
generally  means  a  pile  8  ft.  long 
and  4  ft.  high,  the  price  depend- 
ing on  the  length  of  the  stick. 

278.  Example.    How  many  cords  of  wood  in  a  pile  32  ft.  long, 
8  ft.  wide,  and  4  ft.  high  ? 


SOLUTION. 


4x 


X 


=  8 ;  that  is,  there  are  8  cd.  in  the  pile. 


WRITTEN  EXERCISE 

1.  How  many  cords  in  a  pile  of  wood  60  ft.  long,  4  ft.  wide, 
and  6  ft.  high  ? 

2.  A  pile  of  wood  contains  5  cd.    If  it  is  4  ft.  wide  and  4  ft. 
high,  how  long  is  it  ? 

3.  A  pile  of  tan  bark  contains  150  cd.     If  it  is  4  ft.  wide 
and  8  ft.  high,  how  long  is  it  ? 

4.  A  pile  of  wood  contains  8  cd.     It  is  64  ft.  long  and  as 
high  as  it  is  wide.     What  is  the  height  of  the  pile  ? 

LUMBER 

279.    A  foot   of   lumber,  sometimes  called  a  board  foot,  is   a 

board  1  ft.  long,  12  in.  wide,  and  1  in.  thick,  or  its  equivalent. 
An  exception  to  this  is  made  in  the  measurement  of  boards  less 
than  1  in.  in  thickness.  A  square  foot  of  the  surface  of  such 
boards  is  regarded  as  a  foot  of  lumber  regardless  of  the  thick- 
ness. Boards  more  than  one  inch  in  thickness,  planks,  joists, 
beams,  scantling,  and  sawed  timber  are  generally  measured  by 
the  board  foot. 


216  PEACTICAL   BUSINESS   ARITHMETIC 

Thus,  a  board  12  ft.  long,  12  in.  wide,  and  1  in.  thick  contains  12  sq.ft. 
of  surface,  or  12  board  feet ;  a  board  12  ft.  long,  12  in.  wide,  and  £,  |,  or  |  in. 
thick  contains  12  sq.ft.  of  surface,  or  12  board  feet ;  but  a  board  12  ft.  long, 
12  in.  wide,  and  2|  in.  thick  contains  30  board  feet. 

Scantling  is  timber  3|  in.  wide  and  from  2  in.  to  4  in.  thick;  joists  are 
narrow  and  deep  sticks  of  lumber ;  planks  are  thick  boards ;  lumber  heavier 
than  joists  or  scantling  is  usually  called  timber. 

Except  when  sawed  to  order  and  in  cherry,  black  walnut,  etc.,  where  the 
price  is  15^  a  board  foot  and  upward,  the  width  of  a  board  is  reckoned  only 
the  next  smaller  half  inch.  Thus,  a  board  10 \  in.  wide  is  reckoned  as  10  in., 
and  a  board  lOf  in.  wide  is  reckoned  as  10^  in. 

The  average  width  is  used  in  measuring  boards  that  taper  uniformly. 
Thus,  a  tapering  board  12  ft.  long,  8  in.  wide,  at  one  end  and  6  in.  wide 
at  the  other  and  1  in.  thick  averages  7  in.  wide  and  contains  7  ft.  of 
lumber. 

ORAL   EXERCISE 

1.  How  many  square  feet  in  the  surface  of  a  board  12  ft. 
long,  8  in.  wide,  and  1  in.  thick  ?     How  many  board  feet  ? 

2.  How  many  board  feet  in  a  board  12  ft.  long,  4  in.  wide, 
and  -J  in.  thick  ? 

8 

3.  How  many  feet,  board  measure,  in  a  board  12  ft.  long, 
12  in.  wide,  and  2  in.  thick  ? 

4.  How  many  feet  of  lumber  in  65  boards  each  12  ft.  long, 
6  in.  wide,  and  1  in.  thick  ? 

280.  In  charging  or  billing  lumber  the  number  of  pieces  is 
entered  first ;  then  the  thickness  and  width  in  inches  and  the 
length  in  feet ;  and  finally,  the  article. 

Thus,  in  billing  12  pc.  hemlock,  2  in.  thick,  6  in.  wide,  12  ft.  long,  the 
form  would  be:  12  pc.  2"  x  6",  12',  hemlock. 

ORAL  EXERCISE 

1.  How  many  board  feet  in  6  planks,  1|"  x  12",  14'  ? 

SUGGESTION.     By  inspection  eliminate  12  in  the  dividend. 
Then,  1£  x  6  x  14  =  126,  the  required  number  of  board  feet. 

2.  How  many  feet,  board  measure,  in  6  planks  2"  x  8",  18'  ? 

SUGGESTION.     By  inspection  cancel  a  12  in  the  dividend  (6x2). 
Then,  8  x  18  =  144,  the  required  number  of  feet,"  board  measure. 


PRACTICAL   MEASUEEMEKTS  217 

3.  How  many  feet  of  lumber  in  6  pc.  of  scantling  4"  x  4",  16'  ? 
SUGGESTION.  Mentally  picture  the  problem  arranged  in  form  for  cancellation 
Cancel  a  12  in  the  dividend  (^  of  6~xl).  Then,  2  x  4  x  16, 


12 

or  128,  equals  the  required  number  of  feet  of  lumber. 

4.  How  many  feet  of  lumber  in  5  sticks,  2"  x  6",  16'? 
SUGGESTION.       Mentally    picture    the    problem    in    form    for    cancellation 

(-  -V    Cancel  a  12  in  the  dividend  (&  of  2~x~6).     Then,  5  x  16,  or 

80,  equals  the  required  number  of  feet  of  lumber. 

5.  How  many  feet  of  lumber  in  a  plank  3"xl2",  16'?  in  6 
planks  ?  in  10  planks  ?     How  many  feet  of  lumber  in  a  board 
2"  x  6",  12'  ?  in  5  boards  ?  in  20  boards  ? 

281.  Obviously,  the  number  of  board  feet  in  lumber  1  in.  or 
less  in  thickness  is  -^  of  the  product  of  the  length  in  feet  by  the 
width  in  inches ;  and  the  number  of  board  feet  in  lumber  more 
than  1  in.  in  thickness  is  ^  of  the  product  of  the  length  in  feet 
by  the  width  and  thickness  in  inches.  But  the  work  may  be 
materially  shortened  by  mentally  cancelling  12  from  the  divi- 
dend as  illustrated  in  the  foregoing  exercise. 

ORAL  EXERCISE 

State  the  number  of  feet,  board  measure,  in  the  following  hemlock: 

1.  5  pc.,  3"  x  4",  14'.  is.      12  pc.,  2"  x    8",  18'. 

2.  6  pc.,  2"  x  4",  20'.  14.        6  pc.,  8"  x  10",  20'. 

3.  6  pc.,  2"  x  4",  20'.  15.      30  pc.,  2"  x    6",  20'. 

4.  20  pc.,  2"  x  6",  14'.  16.  6  pc.,  8"  x  10",  21'. 

5.  12  pc.,  2"  x  8",  14'.  17.  25  pc.,  3"  x    8",  14'. 

6.  25  pc.,  3"  x  4",  12'.  18.  10  pc.,  2"  x    6",  13'. 

7.  25  pc.,  2"  x  6",  20'.  19.  15  pc.,  2"  x    6",  18'. 

8.  25  pc.,  3"  x  8",  16'.  20.  15  pc.,  2"  x    6",  12'. 

9.  10  pc.,  3"  x4",  14'.  21.  16  pc.,  2"x    6",  10'. 

10.  10  pc.,  2"  x  8",  18'.  22.      10  pc.,  8"  x  10",  15'. 

11.  14  pc.,  2"  x  6",  20'.  23.      15  pc.,  8"  x  10",  12'. 

12.  10  pc.,  3"  x  6",  20'.  24.    200  pc.,  2"  x    6",  20'. 


218  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN  EXERCISE 

How  many  feet,  board  measure,  in  each  of  the  following  ? 

1.  100. joists,  4"  x  4",  16'.  4.    70  joists,  2"  x  10",  32'. 

2.  65  boards,  f  "  x  6",  12'.          5.      8  beams,  10"  x  10",  24'. 

3.  12  timbers,  8"  x  8",  40'.        6.    10  beams,  12"  x  12",  30'. 

7.  At  $  19  per  M,  find  the  total  cost  of  : 

6  joists,  2"  x  8",  12'.  5  joists,  2"  x  8",  18'. 

12  joists,  2"  x  8",  13'.  17  joists,  2"  x  6",  16'. 

30  joists,  2"  x  8",  15'.  30  joists,  2"  x  8",  16'. 

8.  At  $16  per  M,  find  the  total  cost  of : 

7  beams,  9"  x  9",  20'.  16  beams,  9"  x  9",  18'. 

24  joists,  2"  x  10",  18'.  75  planks,  2J"  x  8",  12'. 

150  boards,  |"  x  5",  12'.  576  boards,  1"  x  9",  16'. 

27  planks,  1J"  x  14",  14'.  40  scantlings,  2"  x  4",  12'. 

9.  Find  the  cost,  at  1 10  per  M,  of  the  lumber  required  to 
fence  both  sides  of  a  railroad  10  mi.  long.     The  boards  used 
are  1"  x  6",  16',  and  the  fence  is  5  boards  high. 

10.  Copy  and  find  the  amount  of  the  following  bill: 

Boston,  Mass.,        Sept.    12,         19 

Mr.    JOHN  D.   MOREY 

Somerville,   Mass. 

Bought  of  E.  M.  LIVINGSTONE  6-  SON 

Terms  30  days   net 


20 

pc. 

3" 

x 

4", 

14'  Hemlock   2801  $15 

.00 

10 

tt 

2" 

X 

6", 

16  f 

it 

12 

.00 

25 

H 

3" 

X 

8", 

16f 

n 

12 

.00 

50 

It 

2" 

X 

4% 

20f 

n 

15 

.00 

16 

tt 

3" 

X 

8% 

14' 

ti 

15 

.00 

25 

n 

2" 

X 

6", 

20' 

n 

12 

.50 

100 

it 

2" 

X 

6", 

18  f 

n 

13 

.50 

PRACTICAL   MEASUREMENTS  219 

CYLINDERS 

282.  A  cylinder  is  a  solid  bounded  by  a  uniformly  curved 
surface  and  two  equal  parallel  circles. 

Two  circles  are  parallel  when  all  the  points  of 
one  are  equally  distant  from  all  the  points  of  the 
other.  The  curved  surface  of  a  cylinder  is  called 
its  lateral  surface  :  the  parallel  circles  its  bases. 

283.  If  the  lateral  surface  of  a  cylinder  be  exactly  covered 
with  paper,  it  will  be  found  that  the  paper  is  in  the  form  of  a 
rectangle  whose  length  and  width  are  equal  to  the  circumfer- 
ence and  height,  respectively,  of  the  cylinder.     Hence, 

The  product  of  the  circumference  and  height  of  a  cylinder  equals 
the  area  of  its  lateral  surface. 


lare  and 

II 


ORAL  EXERCISE 

1.  If  the  accompanying  diagram  is  a  solid  4  ft.  square  and 
12  ft.  high,  what  is  the  area  of  its  six  sides? 

2.  Give  a  brief  rule  for  finding  the  entire  surface 
(lateral  surface  and  bases)  of  a  rectangular  solid  ;  of 
a  cylinder. 

3.  How  many  cubic  feet  in  a  block   2  in.    square 

arid  1  in.  high?  in  a  block  2  in.   square  and  10  in.   high? 

4.  The  area  of  the  base  of  a  cylinder  is  22  ft.     If  the  cylin- 
der is  1  ft.  high,  what  is  its  volume  ?  if  it  is  12  ft.  high  ? 

284.   In  the  foregoing  exercise  it  is  clear  that  the  area  of  the 
base  multiplied   by  the  height  of  the  cylinder  equals  the  volume. 

WRITTEN  EXERCISE 

1.  What  will  be  the  cost,  at  40^  per  cubic  yard,  of  excavat- 
ing for  a  cistern  10  ft.  in  diameter  and  23  ft.  deep  ? 

2.  A  man  dug  a  well  6  ft.  in  diameter  and  38  ft.  deep.     How 
much  should  he  receive  if  he  was  paid  $1  for  each  cubic  yard 
of  earth  removed  ? 

3.  What  will  be  the  cost,  at  12|  ^  per  square  foot,  of  a  sheet- 
iron  smokestack  2J  ft.  in  diameter  and  30  ft.  high  ? 


220  PRACTICAL   BUSINESS   ARITHMETIC 

STONE  WORK 

285.  Stone  work  is  usually  measured  by  the  perch,  which  is 
a  mass  of  stone  16^  ft.  long,  1|  ft.  wide,  and  1  ft.  high,  contain- 
ing 24|  cu.  ft. 

In  some  localities  the  perch  contains  16£  cu.  ft. 

286.  Masonry  is  measured  by  the  cubic  yard  or  the  perch. 

In  measuring  stone  work,  such  as  the  walls  of  cellars  and  buildings, 
masons  take  the  distance  around  the  outside  of  the  wall  (the  girt)  for  the 
length.  In  this  way  the  corners  are  measured  twice,  but  this  is  considered 
offset  by  the  extra  work  required  in  building  the  corners. 

The  work  around  openings,  such  as  doors  and  windows,  is  also  more 
difficult  than  the  straight  work  and  on  this  account  no  allowance  is  usually 
made  for  openings,  unless  they  are  very  large. 

WRITTEN  EXERCISE 

1.  How  many  perches  of  stone  will  be  required  for  an  18-in. 
foundation  72' x  40' x  10'? 

2.  How  many  perches  of  masonry  in  the  18-in.  walls  of  a 
cellar  40' x  30'  x  8' ? 

3.  How  many  cubic  yards  of  masonry  in  the  foundation  walls 
of  a  house  42'  x  32'  if  the  walls  are  21  ft.  wide  and  8  ft.  high? 
(Solve  (a)  by  mason's  and  (6)  by  actual  measure.) 

BRICK  WORK 

287.  A  common  brick  is  8  in.  long,  4  in.  wide,  and  2  in.  thick. 

Bricks  vary  in  size,  but  the  common  brick  may  be  taken  as  a  unit  for 
measuring  brick  work.  Contractors  and  builders  do  not  follow  any  uniform 
rule  for  estimating  the  number  of  bricks  required  for  a  wall.  It  is  suffi- 
ciently accurate,  however,  to  reckon  22  common  bricks,  laid  in  mortar,  for 
each  cubic  foot  of  wall.  In  estimating  material  for  a  brick  wall  actual 
measurements  are  taken  and  an  allowance  made  for  doors  and  windows  and 
other  openings.  In  estimating  labor  girt  measurements  are  taken  and 
usually  a  stated  allowance  made  for  openings  such  as  doors  and  windows. 
The  allowance  to  be  made  for  openings  is  generally  covered  by  contract. 
In  some  localities  a  uniform  number  of  cubic  feet  is  deducted  for  each  open- 
ing ;  in  others  one  half  the  volume  of  all  openings  is  deducted ;  in  still  others 
nothing  whatever  is  deducted. 


PRACTICAL  MEASUREMENTS  221 

WRITTEN  EXERCISE 

1.  How  many  common  bricks  will  be  required  for  a  wall  84 
ft,  long,  16|  ft.  high,  and  1|  ft.  thick  ? 

2.  Find  the  cost  of  the  bricks  required  to  build  a  wall  300  ft. 
long,  12  ft.  high,  and  18  in.  thick,  at  $6  per  thousand. 

3.  How  many  bricks  will  be  required  for  the  four  walls  of  a 
building  80'  x  50'  x  25'  if  the  walls  are  18  in.  thick  and  500 
cu.  ft.  is  allowed  for  openings  ?     (Solve  (#  )  by  mason's  measure, 
making  allowance  for  the  openings,  and  (&  )  by  actual  measure.) 

CAPACITY 
BINS 

288.  The  stricken  bushel  is  used  in  measuring  grain.  The 
heaped  bushel  is  used  in  measuring  such  things  as  large  fruits, 
vegetables,  coal,  and  corn  on  the  cob.  A  stricken  bushel  equals 
2150.42  cu.  in.  A  heaped  bushel  equals  2747.71  cu.  in. 

ORAL  EXERCISE 

1.  How  many  bushels  of  wheat  in  2,150,420  cu.  in.  ? 

2.  State  a  rule   for   finding   the  exact  number   of  stricken 
bushels  in  a  bin.     What  part  of  a  stricken  bushel  is  1  cu.  ft.? 

.8  + 


SOLUTION.     2150.42  cu.  in.  =  I  bu.,  stricken  measure. 


1728  cu.  in.  =  1  cu.  ft.     Therefore,  1  cu.  ft.  =  172800-      2150.42)1728.000 
215042,  or  approximately  .8  of  a  bushel,  stricken  meas-  1720  336 

ure.  7664 

3.  Find  the  approximate  capacity,  in  stricken  bushels,  of  a 
cubical  bin.the  inside  of  which  measures  10  ft.  on  a  side;  in 
cubic  inches  of  800  bu.  of  wheat. 

4.  State  a  brief  rule  for  finding  the  approximate  number  of 
stricken   bushels  in  a  bin ;  the  approximate  number  of  cubic 
feet  in  any  number  of  stricken  bushels. 

5.  How  many  bushels  of  potatoes  in  a  bin  containing  2,747,710 
cu.  in.  ?     State  a  rule  for  finding  the  exact  number  of  heaped 
bushels  in  any  number  of  cubic  inches.      Reduce  a  cubic  foot 
to  a  decimal  of  a  heaped  bushel. 


222  PRACTICAL   BUSINESS   ARITHMETIC 

.63- 

SOLUTION.    2747.71  cu.  in.  =  1  bu.,  heaped  measure.      2747.71)1728.0000 
Therefore,   1  cu.  ft.  =  172800  -=-  274771,  or   approxi-  1648  626 

mately  .63  of  a  bushel,  heaped  measure.  79  8740 

82  4313 

6.  Find   the   approximate    capacity,  in   heaped   bushels,   of 
1000  cu.  ft.;  in  cubic  feet,  of  630  bu. 

7.  State  a  short  method  of  reducing  cubic  feet  to  heaped 
bushels  ;  heaped  bushels  to  cubic  feet. 

8.  Find    (a)    the   approximate  capacity  and   (&)  the  exact 
capacity,  in  stricken  bushels,  of  a  bin  10'  x  5'  x  4'. 

SOLUTIONS 

10'x5'x4'=200cu.ft.  10'x5'x4'  =  200cu.ft. 

(a)  200  x  1728  cu.  in.  =  345600  cu.  in.  .       (6)   >g  Qf  200  cu  ft>  =  m  ^ 

345600  cu.  in.  -~  2150.42  -  165.31  +  bu. 


9.    Find  (a)  the   approximate   capacity  and  (5)  the  exact 
capacity,  in  heaped  bushels,  of  the  bin  in  problem  14. 

SOLUTIONS 

10'  x  5'  x  4'  =  200  cu.  ft.  10,  x  5,  x  4,  =  200  cu  ft 

(a)  200  x  1728  cu.  in.  =  345600  cu.  in.  (&)    63    f        cUj  f    =  m  fe 

345600  cu.  in.  -=-  2747.71  =  125.77  bu. 

ORAL  EXERCISE 

1.  Find  the  approximate  capacity  in  bushels  of  a  wheat  bin 
10  ft.  long,  8  ft.  wide,  and  5  ft.  high. 

2.  A  square  bin  10  ft.  high  contains,  by  approximate  measure- 
ments, 800  bu.     What  is  its  width? 

3.  Approximately,  how  many   bushels  of  potatoes  may  be 
stored  in  a  bin  10  ft.  long,  5  ft.  wide,  and  4  ft.  high  ? 

WRITTEN  EXERCISE 

Find  the  approximate  capacity  in  stricken  bushels  of:- 

1.  A  bin  12  ft.  square  and  4  ft.  deep. 

Inside  dimensions  are  given  in  all  the  problems  of  this  and  similar  exercises. 

2.  A  box  6  ft.  long,  2|  ft.  wide,  and  3|  ft.  deep. 

3.  A  wagon  box  10  ft.  6  in.  long,  4  ft.  wide,  and  2  ft.  deep. 


PRACTICAL   MEASUREMENTS  223 

4.  A  farmer  wishes  to  construct  a  square  granary  15  ft.  on 
each  side  that  will  hold  800  bu.  of  grain.     How  deep  must  the 
bin  be  made?     (Approximate  rule.) 

5.  A  man  wishes  to  construct  a  coal  bin  that  will  store  200 
bu.  of  stove  coal.     If  the  bin  is  20  ft.  wide  and  5  ft.  deep,  what 
must  be  the  length?     (Approximate  rule.) 

6-8.  Find  the  exact  capacity,  in  stricken  bushels,  of  prob- 
lems 1—3. 

9-11.  Find  the  approximate  capacity,  in  heaped  bushels,  of 
problems  1-3. 

CISTERNS 
289.    A  gallon  equals  231  cu.  in. 

ORAL  EXERCISE 

1.  How  many  gallons  in  462  cu.  in.  ?     in  1386  cu.  in.? 

2.  How  many  gallons  of  water  in  a  vat  22  in.  long,  7  in. 
high,  and  3  in.  wide  ? 

3.  Give  a  rule  for  finding  the  exact  number  of  gallons  in  a 
vessel.     How  many  gallons  in  a  cubic  foot  ? 

SOLUTION.  231  cu.  in.  =  1  gal.  1728  cu.  in.  =  1  cu.  ft.  Therefore,  1  cu.  ft. 
=  .yj^s  ga}  _  7.48  -f  gal.,  or  approximately  1\  gal. 

4.  Find  the  approximate  capacity,  in  gallons,  of  a  vat  5  ft. 
square  and  4  ft.  high. 

SOLUTION.     5  f t.  x  5  ft.  x  4  ft.  =  100  cu.  ft.     100  times  7|  gal.  =  750  gal. 

5.  State  a  rule  for  finding  the  approximate  capacity,  in  gal- 
lons, of  a  vessel. 

WRITTEN  EXERCISE 

Find  the  capacity  (approximate  and  exact),  in  gallons,  of: 

1.  A  cistern  6  ft.  square  and  12  ft.  deep. 

2.  A  cistern  6  ft.  in  diameter  and  10  ft.  deep. 

3.  A  tank  5  ft.  long,  4  ft.  wide,  and  6  ft.  deep. 

4.  A  cistern  15  ft.  in  diameter  and  20  ft.  deep. 


224  PRACTICAL   BUSINESS   ARITHMETIC 

CALCULATION   TABLES 

290.  Persons  who   have  a   great   deal   of   computing   to  do 
frequently  use  machines  (see  pages  47  and  55)  and  calculation 
tables  to  aid  them  in  their  work.     The  table  on  page  225  will 
give  a  good  idea  of  the  arrangement  of  calculation  tables  that 
are  used  in  making  up  and  proving  bills  and  invoices,  comput- 
ing wages,  finding  percentages,  etc.     The  following  examples 
will  illustrate  a  few  of  the  many  uses  of  such  tables. 

291.  Examples.     1.    Multiply  58  by  42. 

SOLUTION.     Under  58  and  opposite  42  find  2436. 

2.  How  many  square  yards  in  a  floor  38'  x  46'  ? 
SOLUTION.     Under  46  and  opposite  38  find  1748  ;  that  is,  1748  sq.  yd. 

3.  Find  the  cost  of  495  yd.  wash  silk  at  39^. 
SOLUTION.     Under  495  and  opposite  39  find  19,305  ;  that  is,  $  193.05. 

4.  Find  the  cost  of  48,000  bricks  at  14.95  per  M. 

SOLUTION.    Under  495  and   opposite  48  find  23,760.     Since   the   zeros    in 
48,000  have  been  rejected,  there  are  but  two  places  to  point  off.     Result  $  2:)7.00. 

5.  Find  the  cost  of  46  hr.  of  labor  at  25|  ^  per  hour. 

SOLUTION.     Under  46  and   opposite  25  find  1150   (•$  11.50);   under  46  and 
opposite  |  find  34.50  (35^).     $  11.50  +  35  $  =  $  11.85,  the  required  result. 

ORAL  EXERCISE 

By  the  aid  of  the  table  state  the  product  of: 


1. 

27  x 

26. 

5. 

39  x 

27. 

9. 

87 

x 

46^. 

13. 

35 

2. 

27  x 

58. 

6. 

45  x 

58. 

10. 

93 

x 

32^. 

14. 

93 

3. 

45  x 

46. 

7. 

37  x 

46. 

11. 

48 

x 

93^. 

15. 

46 

4. 

47  x 

39. 

8. 

49  x 

58. 

12. 

47 

x 

87^. 

16. 

38 

17.  Find  the  cost  of  49,500  Ib.  of  old  rags  at  \$. 

18.  Find  the  cost  of  93,000  bricks  at  15.25  per  M. 

19.  Find  the  cost  of  37  days'  labor  at  11.35  per  day ;  at  $5.25. 

20.  Find  the  cost  of  109  hours'  labor  at  27^;   at  39^;   at  46  £ 

21.  Find  the  cost  of  49,500  Ib.  freight  at  31^  per  hundred- 
weight; of  46,000  Ib.  at  27^  per  hundredweight. 


PRACTICAL   MEASUREMENTS 


225 


CALCULATION  TABLE 


Haiti 
plier 

27 

39 

46 

58 

Multi- 
plier 

87 

93 

109 

138 

Multi- 
plier 

135 

147 

495 

535 

Multi- 
plier 

1 

27 

39 

46 

58 

1 

87 

93 

109 

128 

1 

135 

147 

495 

525 

1 

3 

54 

78 

92 

116 

3 

174 

196 

218 

256 

3 

270 

294 

990 

1050 

3 

3 

81 

117 

138 

174 

3 

261 

279 

327 

384 

3 

405 

441 

1485 

1575 

3 

4 

108 

156 

184 

232 

4 

348 

372 

436 

512 

4 

540 

588 

1980 

2100 

4 

5 

135 

195 

230 

290 

5 

435 

465 

545 

640 

5 

675 

735 

2475 

2625 

5 

6 

162 

234 

276 

348 

6 

522 

558 

654 

768 

6 

810 

882 

2970 

3150 

6 

7 

189 

273 

322 

406 

7 

609 

651 

763 

896 

7 

945 

1029 

3465 

3675 

7 

8 

216 

312 

368 

464 

8 

696 

744 

872 

1024 

8 

1080 

1176 

3960 

4200 

8 

9 

243 

351 

414 

522 

9 

783 

837 

981 

1152 

9 

1215 

1323 

4455 

4725 

9 

10 

270 

390 

460 

580 

1O 

870 

930 

1090 

1280 

10 

1350 

.  1470 

4950 

5250 

1O 

11 

297 

429 

506 

638 

11 

957 

1023 

1199 

1408 

11 

1485 

1617 

5445 

5775 

11 

13 

324 

468 

552 

696 

13 

1044 

1116 

13-i8 

1536 

13 

1620 

1764 

5940 

6300 

13 

13 

351 

507 

.598 

754 

13 

1131 

1209 

1417 

1664 

13 

1755 

1911 

6435 

6825 

13 

14 

378 

546 

644 

812 

14 

1218 

1302 

1526 

1792 

14 

1890 

2058 

6930 

7350 

14 

15 

405 

585 

690 

870 

15 

1305 

1395 

1635 

1920 

15 

2025 

2205 

7425 

7875 

15 

16 

432 

624 

736 

928 

16 

1392 

1488 

1744 

2048 

16 

2160 

2352 

7920 

84'  '0 

16 

17 

459 

663 

782 

986 

17 

1479 

1581 

1853 

2176 

17 

2295 

2499 

8415 

8925 

17 

18 

486 

702 

828 

1044 

18 

1566 

1674 

1962 

2304 

18 

2430 

2646 

8910 

9450 

18 

19 

513 

741 

874 

1102 

19 

1653 

1767 

2071 

2432 

19 

2565 

2793 

9405 

9975 

19 

20 

540 

780 

920 

1160 

3O 

1740 

1860 

2180 

2560 

20 

2700 

2940 

9900 

10500 

3O 

21 

567 

819 

966 

1218 

31 

1827 

1953 

2289 

2688 

31 

2835 

3087 

10395 

11025 

31 

22 

594 

858 

1012 

1276 

33 

1914 

2046 

2398 

2816 

33 

2970 

3234 

10890 

11550 

23 

23 

621 

897 

1058 

1334 

33 

2001 

2139 

2507 

2944 

33 

3105 

3381 

11385 

12075 

23 

24 

648 

936 

1104 

1392 

34 

2088 

2232 

2616 

3072 

34 

3240 

3528 

11880 

12600 

24 

25 

675 

975 

1150 

1450 

35 

2175 

2325 

2725 

3200 

35 

3375 

3675 

12375 

13125 

25 

36 

702 

1014 

1196 

1508 

26 

2262 

2418 

2834 

3328 

36 

3510 

3822 

12870 

13650 

26 

27 

729 

1053 

1242 

1566 

37 

2349 

2511 

2943 

3456 

27 

3645 

3969 

13365 

14175 

27 

28 

756 

1092 

1288 

1624 

38 

2436 

2604 

3052 

3584 

28 

3780 

4116 

13860 

14700 

28 

29 

783 

1131 

1334 

1682 

39 

2523 

2697 

3161 

3712 

29 

3915 

4263 

14355 

15225 

29 

3O 

810 

1170 

1380 

1740 

30 

2610 

2790 

3270 

3840 

30 

4050 

4410 

14850 

15750 

3O 

31 

837 

1209 

1426 

1798 

31 

2697 

2883 

3379 

3968 

31 

4185 

4557 

15345 

16275 

31 

33 

864 

1248 

1472 

1856 

32 

2784 

2976 

3488 

4096 

33 

4320 

4704 

15840 

16800 

32 

33 

891 

1287 

151« 

1914 

33 

2871 

3069 

3597 

4224 

33 

4455 

4&51 

16335 

17325 

33 

34 

918 

1326 

1564 

1972 

34 

2958 

3162 

3706 

4352 

34 

4590 

4998 

16830 

17850 

34 

35 

945 

1365 

1610 

2030 

35 

3045 

3255 

3815 

4480 

35 

4725 

5145 

17325 

18375 

35 

36 

972 

1404 

1656 

2088 

36 

3132 

3348 

3924 

4608 

36 

4860 

5292 

17820 

18900 

36 

37 

999 

1443 

1702 

2146 

37 

3219 

3441 

4033 

4736 

37 

4995 

5439 

18315 

19425 

37 

38 

1026 

1482 

1748 

2204 

38 

3306 

3534 

4142 

4864 

38 

5130 

5586 

18810 

19950 

38 

39 

1053 

1521 

1794 

2262 

39 

3393 

3627 

4251 

4992 

39 

5265 

5733 

19305 

20475 

39 

4O 

1080 

1560 

1840 

2320 

40 

3480 

3720 

4360 

5120 

40 

5400 

5880 

19800 

21000 

•10 

41 

1107 

1599 

1886 

2378 

41 

3567 

3813 

4469 

5248 

41 

5535 

6027 

20295 

21525 

41 

43 

1134 

1638 

1932 

2436 

42 

3654 

3906 

4578 

5376 

43 

5670 

6174 

20790 

22050 

42 

43 

1161 

1677 

1978 

2494 

43 

3741 

3999 

4687 

5504 

43 

5805 

6321 

21285 

22575 

43 

44 

1188 

1716 

2024 

2552 

44 

3828 

4092 

4796 

5632 

44 

5940 

6468 

21780 

23100 

44 

45 

1215 

1755 

2070 

2610 

45 

3915 

4185 

4905 

5760 

45 

6075 

6615 

22275 

23625 

45 

46 

1242 

1794 

2116 

2668 

46 

4002 

4278 

5014 

5888 

46 

6210 

6762 

22770 

24150 

46 

47 

1269 

1833 

2162 

2726 

47 

4089 

4571 

5123 

6016 

47 

6345 

6909 

23265 

24675 

47 

48 

1296 

1872 

2208 

2784 

48 

4176 

4464 

5232 

6144 

48 

6480 

7056 

23760 

25200 

48 

49 

1323 

1911 

2254 

2842 

49 

4263 

4557 

5341 

6272 

49 

6615 

7203 

24255 

25725 

49 

50 

1350 

1950 

2300 

2900 

5O 

4350 

4650 

5450 

6400 

50 

6750 

7350 

24750 

26250 

5O 

Multi- 
plier 

37 

39 

46 

58 

Multi- 
plier 

87 

93 

109 

138 

Multi- 
plier 

135 

147 

495 

535 

Multi- 
plier 

% 

338 

488 

575 

725 

% 

1088 

1163 

1363 

1600 

% 

1688 

1838 

6188 

6563 

¥e 

¥4 

675 

975 

1150 

1450 

% 

21  75 

2325 

2725 

32  00 

¥4 

3375 

3675 

123  75 

131  25 

V4 

% 

1013 

1463 

1725 

2175 

% 

:;•_>  i;;; 

3488 

4088 

4800 

% 

5063 

5513 

18563 

19688 

% 

¥2 

1350 

1950 

2300 

2900 

X 

4350 

4650 

5450 

6400 

¥2 

6750 

7350 

24750 

262  5'.' 

¥2 

% 

1688 

2438 

2875 

3625 

% 

5438 

5813 

6813 

8000 

% 

8438 

9188 

10938 

32813 

% 

% 

2025 

2925 

3450 

4350 

% 

6525 

6975 

8175 

9600 

3/4 

10125 

11025 

37125 

S93  75 

8/4 

% 

2363 

3413 

4025 

5075 

% 

7613 

8138 

9538 

11200 

T/8 

11813 

12863 

43313 

45938 

% 

226 


PRACTICAL   BUSINESS   ARITHMETIC 


22.  Find  the  cost  of  48,000  ft.  of  lumber  at  $16  per  M  ;  of 
93,000  ft.  ;  of  52,500  ft. ;  of  49,500  ft. ;  of  58,000  ft. 

23.  An  agent  sold  240  (10  x  21)  excursion  tickets  at  $4.95. 
How  much  did  he  receive  ?     360  x  $5.25  =  ?     310  x  $1.47  =  ? 

24.  Find  the  cost  of  45  rm.  of  paper  at  $1.35  ;   at  $  1.28  ;  at 
$1.09;  at  93^;  at  $4.95.     Also  find  the  cost  of  38  rm.  at  each 
of  the  above  prices ;   of  29  rm.  ;   of  37  rm. ;  of  46  rm. 

25.  Find  the  cost  of  4600  lb.  of  coal  at  $6.40  per  ton  ($3.20 
per  thousand  pounds)  ;  at  $8.40  ;  at  $4.60  ;  at  $  6.80  ;  at  $7.20 ; 
at  $7.40;   at  $9.20;  at  $5.60.     Also  find  the  cost  of  2700  lb. 
at  each  of  the  above  prices  ;  of  3900  lb. ;  of  8700  lb.;  of  9300  lb.; 
of  10,900  lb.;   of  12,800  lb.;  of  13,500  lb.;   of  14,700  lb.;  of 
49,500  lb.;  of  52,500  lb. 

WRITTEN  EXERCISE 

1.  By  the  aid  of  the  table  find  the  total  cost  of  : 

525  bolts  at  $1.70  per  C.  128  bolts  at  $1.90  per  C. 

495  bolts  at  $2.40  per  C.  525  bolts  at  $2.70  per  C. 

135  bolts  at  $1.60  per  C.  495  bolts  at  $3.50  per  C. 

2.  By  the  aid  of  the  table  find  the  total  cost  of : 

1280  ft.  lumber  at  $28  per  M.  5250  ft.  lumber  at  $27  per  M. 
1350  ft.  lumber  at  $29  per  M.  3800  ft.  lumber  at  $27  per  M. 
4950  ft.  lumber  at  $19  per  M.  4600  ft.  lumber  at  $18  per  M. 

3.  By  the  aid  of  the  table  find  the  total  amount  of  the  follow- 
ing time  sheet : 

TIME  SHEET  FOR  WEEK  ENDING  JULY  14 


NAME 

M. 

T. 

W. 

T. 

F. 

8. 

TOTAL 
TIME 

KATK 

PER 

Horn 

AMOUNT 

A.  M.  Ball 

8* 

9 

71 

8 

8 

8 

27^ 

J.  B.  King 

8* 

7| 

9 

8 

8 

8 

390 

C.  E.  Frey 

91 

9 

8f 

8 

7 

5 

46^ 

W.  D.  Hall 

7 

9 

8 

8 

8 

8 

58  j* 

M.  F.  Hill 
I).  M.  Muir 

9f 
8J 

n 

7 

8 

8 

8 
6f 

87^ 
93^ 



PERCENTAGE   AND   ITS   APPLICATIONS 
CHAPTER  XVII 

PERCENTAGE 
ORAL  EXERCISE 

1.  .50  may  be  read  fifty  hundredths,  one  half,  or  fifty  per 
cent.     Read  each  of  the  following  in  three  ways  :  .25,  .30, 12|% . 

2.  Read  each  of  the  following  in  three  ways  :  ^,  J,  ^,  ^,  £%, 
f,  f,  i,  f,  f,  2  %,  2|-%,  125%,  6-|-%,  81%,  66J  %,  250%,  375%. 

3.  50  %  of  a  number  is  .50  or  |--of  the  number.     What  is 
50%  of  1600?    25%?    121%?    10%  ?    40%?    20%?    75%? 

292.  Per  cent  is  a  common  name  for  hundredths. 

293.  The  symbol  %  may  be  read  hundredths  or  per  cent. 

294.  Percentage  is  the  process  of  computing  by  hundredths 
or  per  cents. 

ORAL  EXERCISE 

Express  as  per  cents  : 

1.  .28.         3.    .001.  5.    .331.          7.    .621.          9.    .5. 

2.  .37.        4.    .14f          6.    .28f         8.    .0075.      10.    .2. 
Express  as  decimal  fractions  : 

11.  20%.    13.    72%.        15.    1%.         17.    125%.      19.    ^%. 

12.  45%.    14.    18%.        16.    \%.         is.    250%.     20.    375%. 
Express  as  common  fractions  : 

21.  1%.        23.     21%.          25.     1331%.    27.     871%.       29.     1%. 

22.  2%.        24.     31%.          26.     266|%.    28.     1121%.     30.     175%. 
Express  as  per  cents  : 

31.  1  33.     TV  35.     If  37.    f.  39.     |, 

32.  1.  34.     T97.  36.     2f.  38.    If  40.    -%4-. 

227 


228 


PRACTICAL   BUSINESS   ARITHMETIC 


IMPORTANT  PER  CENTS  AND  THEIR  FRACTIONAL  EQUIVALENTS 


PER 
CENT 

FKAOTfONAL 

VAWM 

PER 
CENT 

FRACTIONAL 
VALIE 

PER  ' 

CKNT 

FRACTIONAL 

\  ALUE 

PER 
CENT 

FRACTIONAL 
VALUE 

12*  % 

* 

75% 

t 

83  J% 

1 

<U% 

A 

25% 

I 

100% 

1 

20% 

i 

8f% 

A 

37*% 

t 

l«i% 

1 

40% 

1 

»*% 

A 

50% 

i 

33  J% 

i 

60% 

t 

1H% 

i 

62*% 

f 

06f% 

1 

80% 

t 

i^% 

f 

295.  The  terms  us^d    in  percentage  are  the  base,  the  rate, 
and  the  percentage.      The  base  is  the  number  of  which  a  per 
cent  is  taken  ;  the  rate,  the  number  of  hundredths  of  the  base 
to  be  taken  ;   tha  percentage,  the  result   obtained  by  taking  a 
certain  per  cent  of  the  base. 

In  the  expression  "12  %  of  $50  is  $  6,"  f  50  is  the  base,  12  %,  the  rate,  and 
$6,  the  percentage. 

296.  The  base  plus  the  percentage  is  sometimes  called  the 
amount  ;  the  base  minus  the  percentage,  the  difference. 

FINDING    THE    PERCENTAGE 

297.  Example.     What  is  15  %  of  1 660  ? 

SOLUTION.     15  %  of  a  number  equals  .15  of  it.     .15  of  $660  = 
$  99,  the  required  result. 

899.00 

298.  Obviously,  the  product  of  the  base  and  rate  equals  the 
percentage. 

The  bane  may  be  either  concrete  or  abstract.     The  rate  is  always  abstract. 
The  percentage  is  always  of  the  same  name  an  the  base. 

ORAL  EXERCISE 

1.  What  aliquot  part  of  1  is  .121  ?    >25?    .50?    .16|  ?   .831? 
.20?  .06J?  .06f?  .081?  .111?  .14f?  371  %?  621  %?  66f  %  ? 

2.  Formulate  a  short  method  for  finding  12^  %  of  a  number. 
SOLUTION.     12|  %  =  .12£  =  £  ;  hence,  to  find  12J  %  of  a  number,  divide  by  8. 

3.  State    a   short    method    for   finding   25%   of   a  number; 
50%;     16|%;    331%;    20%;     6J  % ;    6f  %  ;     81%;    111%. 


.15 


PERCENTAGE  229 

To  guard  against  absurd  answers  in  exercises  of  this  character  estimate 
the  results  in  advance  as  explained  on  pages  58  and  142. 

4.  Find    50%    of    960.      Also    25%;   37J%;   12}%;   621%; 
75%;   16f%;   331%;   66|%;   831%;   20%f40%;   60%;   6J%. 

5.  By  inspection  find  : 

a.  50%  of  1792.  e.  25%  of  §1729.  i.    66f  %  of  2460. 

b.  37-i%  of  1320.  /.  6f%of$6600.  j.    331%  of  2793. 

c.  12J%  of  ^ggo.  ^  6i^  of  3296.  k.   81%  of  24,960. 

d.  16f%of$669.  h.  831%  of  4560.  i   20%  of  12,535. 

ORAL    EXERCISE 

1.  Find  10%  of  720;    of  $15.50;    of  120  men ;   of  $127.50. 

2.  What  aliquot  part  of  10%  is  5%  ?  2}%?  1|%?  3|%?  If  %? 

3.  Formulate  a  short  method  for  finding  1J-  %  of  a  number. 

SOLUTION.     11%  of  a  number  is  |-  of  10%  of  the  number  ;  hence,  to  find 
of  a  number,  point  off  one  place  to  the  left  and  divide  by  8. 

4.  State  a  short  method  for  finding  5  %  of  a  number; 


5.    By  inspection  find  : 

a.  5%  of  720.              d.   l\%  of  1840.  g.  3J%  of  $3900. 

b.  2|  %  of  840.            e.   If  %  of  $366.  h.  1  j  %  of  120  mi. 

c.  31%  of  1560.         /.    2|-%  of  $720.  i.  \\%  Of  1632  A. 

ORAL   EXERCISE 

'I.    Compare  24%  of  $25  with  25%  of  $24;    21%  of  $2500 
with  25  %  of  $2400.     What  is  32  %  of  $25  ? 

SOLUTION.    32  %  of  §  25  =  25  %  of  $  32  =  \  of  $  32  =  $  8,  the  required  result. 

2.  What  is  125%  of  $880? 

SOLUTION.     125%  =  1.25  =|  of   10;   \  of  $8800  (10  times  $880)  -$1100. 

3.  Find  125%    of  400;  of  640;   of  3200 ;   of  160;   of  1280. 

4.  Formulate  a  short  method  for  finding  166f  %  of  a  num- 
ber ;  333-J  %  of  a  number ;   250  %  of  a  number. 

5.  Compare  88%  of  12,500  bu.  with  125%  of  8800  bu. 

6.  Find  32%  of  $125;   of  $1250;   of  $12,500;   of  $125,000. 

7.  Find  250%  of  $720;   of  $3200;   of  $28,800;   of  $64,800. 


230  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

By  inspection  find : 

1.  48%  of  250.  5.  180%  of  625. 

2.  32%  of  125.  6.  160%  of  875. 

3.  128%  of  250.  7.  240%  of  7500. 

4.  16%  of  2500.  8.  125  %  of  $240.40. 

WRITTEN  EXERCISE 

1.  A  farmer  sold  640  bu.  wheat,  receiving  $1.05  per  bushel 
for  87|%  of  it  and  85^  per  bushel  for  the  remainder.     What 
was  the  total  amount  received  ? 

2.  A  grocer  compromised  with  his  creditors,  paying  60  %  of 
the  amount  of  his  debts.     If  he  owed  A  $  756,  B  11250,  and  C 
$3750,  how  much  did  each  receive  ? 

3.  A  merchant  sold  360  bbl.  apples  for  $1200.     If   he  re- 
ceived $3.50  per  barrel  for  66|  %  of  the  apples,  what  was  the 
price  received  per  barrel  for  the  remainder  ? 

4.  A  man  bought  a  house  for  $12,864.75;  he  expended  for 
improvements  33^  %  of  the  first  cost  of  the  property,  and  then 
sold  it  for  $20,000.     Did  he  gain  or  lose,  and  how  much  ? 

5.  A  commission    merchant   bought   1200  bbl.    apples   and 
after  holding  them  for  3   mo.  found  that  his  loss  from  decay 
was  10%.     If  he  sold  the  remainder  at  $3.75  per  barrel,  how 
much  did  he  receive  ? 

6.  A  merchant  prepaid  the  following  bills  and  received  the 
per  cents  of  discount  named:  4%   on  bill  of  $875.50;   6  %  on 
bill  of  $378.45;  2%  on  bill  of  $940.50;  3-J  %  on  bill  of  $400. 
What  was  the  net  amount  paid  ? 

FINDING   THE   RATE 

ORAL  EXERCISE 

1.  8  is  what  part  of  40  ?  what  per  cent  of  40  ? 

2.  90  is  what  per  cent  of  270  ?  of  360  ?  of  450  ? 

3.  70  is  what  per  cent  of  560  ?  of  630  ?  of  700  ? 

4.  The  base  is  900  and  the  percentage  450 ;  what  is  the  rate  ? 


PERCENTAGE  231 

299.  Example.    $35.50  is  what  per  cent  of  1284? 

SOLUTIONS,     a.   $35.50  is  .»ff g-  or  \  of  (a) 

$284.     $284   is   100%  of    itself;    hence,  £55  0  =  1  =  ^1  of 
$35.50,  which  is  i  of  $284,  must  be  \  of 

100%,  or  121%.     Or,  (&) 

6.    Since  the  product  of  the  base   and  .125  =  12^-% 

the   rate   is  the  percentage,  the   quotient  284)35.50 
obtained  by  dividing  the  percentage  by  the  base  is  the  rate. 

300.  Obviously,  the  percentage  divided  by  the  base  equals  the 
rate. 

ORAL  EXERCISE 

What  per  cent  of: 

1.  95  is  19?  7.  1.6  is  .008? 

2.  4.8  is  1.2?  8.  lyd.  is  1  ft.? 

3.  |35  is  |17l  ?  9.  2  da.  are  8  hr.  ? 

4.  225  A.  are  75  A.  ?  10.  4  T.  are  3000  Ib.  ? 

5.  34  bu.  are  34  bu.  ?  11.  1  yr.  are  4  mo.  ? 

6.  34  bu.  are  68  bu.  ?  12.  2  mi.  are  80  rd.? 

WRITTEN   EXERCISE 

1.  A  man  bought  a  house  for  87500  and  sold  it  for  18700. 
What  per  cent  did  he  gain  ? 

2.  In  a  certain  city,  school  was  in  session  190  da.     A  lost  38 
da.     What  per  cent  of  the  school  year  did  he  attend? 

3.  An  agent  sold  a  piece  of  property  for  $8462.50  and  re- 
ceived  $338.50    for   his   services.      What    per    cent   did   he 
receive  ? 

4.  A  commission   agent  sold  28,600  bu.  of  grain  at  50  f  per 
bushel  and  received  for  his  services  $357.50.     What  per  cent 
did  he  receive  on  the  sales  made  ? 

5.  Smith  and  Brown  engaged  in  business,  investing  $18,000. 
Smith  invested  $10,440,  and  Brown  the  remainder.     What  per 
cent  of  the  total  capital  did  each  invest? 

6.  An  agent  for  a  wholesale  house  earned  $165.55  during 
the  month  of  May.    If  the  goods  sold  amounted  to  $  1505,  what 
per  cent  did  he  receive  on  the  sales  made  ? 


232  PRACTICAL   BUSINESS  ARITHMETIC 

FINDING   THE   BASE 

ORAL  EXERCISE 

1.  What  is  5%  of  240  bu.  ? 

2.  12  bu.  is  5  %  of  how  many  bushels  ? 

3.  160  is  8  %  of  what  number  ?  4  %  ?  2  %  ?  1  %  ?  |  %  ? 

4.  The  multiplicand  is  400  and  the  multiplier  10;   what  is 
the  product?     The  product  is  2000  and  the  multiplicand  100; 
what  is  the  multiplier?     The  product  is  4000  and  the  multi- 
plier 20  ;    what  is  the  multiplicand  ? 

5.  In  percentage  what  name  is  given  to  the  product  ?  to 
the  multiplicand?  to  the  multiplier?     When  the  base  and  rate 
are  given,  how  is  the  percentage  found  ?     When  the  percentage 
and  base  are  given,  how  is  the  rate  found  ?  When  the  per- 
centage and  rate  are  given,  how  is  the  base  found  ? 

ORAL  EXERCISE 

1.  25  is  J  of  what  number  ?    25  is  50  %  of  what  number? 

2.  12  is  T^  of  what  number  ?    24  is  6|  %  of  what  number  ? 

3.  25  is  y1^  of  what  number  ?    35  is  8J  %  of  what  number  ? 

4.  900  is  |  of  what  number  ?    600  is  75  %  of  what  number  ? 

5.  130  is  I  of  what  number  ?  1300  is  20  %  of  what  number  ? 

6.  444  is  |  of  what  number  ?  44.40  is  80  %  of  what  number  ? 

7.  960  is  |  of  what  number?    96  is  66f  %  of  what  number? 

8.  65  is  §  of  what  number  ?    650  is  83^  %  of  what  number  ? 

9.  15  is  TL  of  what  number  ?    150  is  6  j  %  of  what  number  ? 

10.  100  is  J  of  what  number  ?    60  is  11^  %  of  what  number  ? 

11.  20  is  |  of  what  number  ?    200  is  14|  %  of  what  number  ? 

12.  375  is  |  of  what  number  ?    2700  is  37*  %  of  what  number? 

13.  Anything  is  what  per  cent  of  itself  ?  of  J  itself  ?  of  twice 
itself?  of  |  itself?  of  2J  times  itself? 

14.  A  farmer  sold  a  horse  for  66|  %  of  its  cost  and  received 
$80.     How  much  did  the  horse  cost? 

15.  20  %  of  the  students  of  a  high  school  are  18  yr.  of  age. 
If  there  are  170  such  students,  what  is  the  aggregate  attend- 
ance of  the  school  ? 


PEKCENTAGE  233 

301.  Example.    37.5  is  25%  of  what  number? 

SOLUTION.     25%  or  ^  of  the  number  =  37.5 
.  •.  the  number  =  37.5  -f-  £  =  150. 

302.  Obviously,  the  quotient  of  the  percentage  divided  by  the 
rate  equals  the  base. 

WRITTEN  EXERCISE 

1.  N  invested  30%  of  the  capital  of  a  firm,  H  35%,  and  W 
the  remainder,  $  1400.     What  was  the  capital  of  the  firm? 

2.  During  the  month  of  May  the  sales    of  a  clothing  mer- 
chant amounted  to  $4864.24,  which  was  8  %  of  the  total  sales 
for  the  year.    What  were  the  total  sales  for  the  year? 

3.  B  sold  his  city  property  and  took  a  mortgage  for  $4375, 
which  was  17 \%  of  the  value  of  the  property.     If  the  balance 
was  paid  in  cash,  what  was  the  amount  of  cash  received  ? 

4.  In  compromising  with  his  creditors,  a  man  finds  that  his 
assets  are  $270,900,  and  that  this  sum  is  43%  of  his  entire  in- 
debtedness.     What  will  be  the  aggregate  loss  to  his  creditors? 

5.  The  aggregate  attendance  in  the  schools  of  a  certain  city 
for  1  da.  was  43,225  students.     If  this  number  was  95%  of  the 
number  of  students  belonging,  how  many  students  were  absent? 

6.  The  owner  of  city  property  received  in  rentals  last  year 
$1221.95.     He  paid  for  insurance  $75,  for  repairs  $353.75,  and 
for  taxes  $175.20.     If  his  net  income  was  equal  to  5%  of  the 
money  invested,  what  was  the  value  of  the  property? 

7.  A  man  bought  a  suit  of  clothes  for  $22.50,  a  pair  of  shoes 
for  $5,  a  hat  for  §4,  and  a  watch  for  $18.75,  when  he  found  he 
had  expended  12^%  of  his  money.     How  much  money  had  he 
at  first  ?    How  much  had  he  left  after  making  these  purchases  ? 

8.  In  a  recent  year  there  were  5,737,372  farms  in  the  United 
States   having   a   total   acreage   of   831,591,744  A.,  of   which 
414,498,487  A.  were  improved  and  424,093,287  A.  were  unim- 
proved.    What  was  the  average  number  of  acres  to  a  farm? 
What  per  cent  of  farm  land  was  improved  ?     What  per  cent 
was  unimproved?     (Correct  to  three  decimal  places.) 


234  PRACTICAL   BUSINESS   ARITHMETIC 

PER  CENTS   OF  INCREASE 

ORAL  EXERCISE 

1.  If  2|  times  a  number  is  50,  what  is  the  number? 

2.  If  2.5  times  a  number  is  75,  what  is  the  number? 

3.  If  250%  of  a  number  is  $1250,  what  is  the  number? 

4.  If  250%  of  a  number  is  150,   what  is  the  number?     If 
250%  is  125,  what  is  the  number? 

5.  If  300%  of  a  number  is  15400,  what  is  the  number? 

303.    Examples,     l.    A    man    sold    a   farm    for    $3900    and 
thereby  gained  30%.     How  much  did  the  farm  cost? 

SOLUTION.     1.30  of  the  cost  =  $3900. 

.  •.  the  cost  =  $3900  -4- 1.30  =  $  3000. 

2.    What  number  increased  by  33J%  of  itself  equals  180? 

SOLUTION,     f  of  the  number  =  180 

.  •.  the  number  =  180  •*-  f  =  135. 

ORAL  EXERCISE 

What  number  increased  by: 

1.  10%  of  itself  is  220?  8.  6|%  of  itself  is  480? 

2.  25%  of  itself  is  125?  9.  125%  of  itself  is  900? 

3.  50%  of  itself  is  300?  10.  37 \%  of  itself  is  440? 

4.  75%  of  itself  is  700?  11.  111%  Of  itself  is  300? 

5.  6J%  of  itself  is  170?  12.  14f  %  of  itself  is  328? 

6.  12i%  of  itself  is  180?  13.  200%  of  itself  is  2700? 

7.  66f  %  of  itself  is  135?  14.  300%  of  itself  is  2800? 

WRITTEN  EXERCISE 

1.  I  sold  375  bu.  of  wheat  for  $427.50,  thereby  gaining  20%. 
How  much  did  the  wheat  cost  me  per  bushel? 

2.  A  fruit  dealer  sold  a  quantity  of  oranges  for  16.75.     If 
his  gain  was  12^%,  what  did  the  oranges  cost  him? 

3.  My  savings  for  March  increased  33^%  over  February.     If 
my  savings  for  March  were  $84.36,  what  were  my  savings  for 
February  and  March? 


PERCENTAGE  235 

4.  A  merchant  sold  a  quantity  of  cloth  at  $1.5Q  per  yard 
and   thereby   gained   20%.     What   per   cent   would   he   have 
gained  had  he  sold  the  cloth  at  $1.87J  per  yard? 

5.  A  merchant's  total  sales  for  this  year  were  12^%  greater 
than  his  sales  for  last  year.     What  were  his  sales  for  this  year 
if  the  aggregate  sales  for  the  two  years  amounted  to  1170,000? 

6.  A  man  paid  142.50  for  a  second-hand  wagon  and  after 
spending  120.50  in  repairs  on  it  he  found  that  it  had  cost  him 
5%  more  than  a  new  wagon.     What  would  have  been  the  cost 
of  a  new  wagon? 

PER  CENTS   OF  DECREASE 

ORAL   EXERCISE 

1.  What  per  cent  of   a  number   is  left  after   taking  away 
331%  of  it  ?     What  fractional  part? 

2.  If  f  of  a  number  is  600,  what  is  the  number  ?     If  66|  %  of 
a  number  is  75,  what  is  the  number  ? 

3.  A  man  spent  40  %  of  his  money  and  had  $60  remaining. 
How  much  had  he  at  first  ?    How  much  did  he  spend? 

304.    Examples.     1.    A  man  sold  a  horse  for  $332,  thereby 
losing  17  %.     What  was  the  cost  ? 

SOLUTION.     0.83  of  the  cost =$332. 

.  •.  the  cost  =  $  332  -=-  0.83  =  $  400. 

2.    What  number  decreased  by  25  %  of  itself  equals  375  ? 

SOLUTION,     f  of  the  number  —  f  375. 

.  •.  the  number  =  $  375  -^  f  =  $  500. 

ORAL  EXERCISE 

What  number  diminished  by: 

1.  61  %  of  itself  equals  75  ?  7.1  of  itself  equals  750  ? 

2.  8J%  of  itself  equals  440?  8.    1%  of  itself  equals  99.5? 

3.  6f  %  of  itself  equals  280?  9.    1%  of  itself  equals  49.5? 

4.  10%  of  itself  equals  270?  10.    25%  of  itself  equals  225? 

5.  331  %  of  itself  equals  66  ?  11.    50  %  of  itself  equals  17|  ? 

of  itself  equals  210  ?      12.    75  %  of  itself  equals  250  ? 


236 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN   EXERCISE 

1.  Of  what  number  is  9581.88   77  %  ? 

2.  A  merchant   sold  1200  bu.   of  potatoes  for  1640,  which 
was  16J%  less  than  he  paid  for  them.   What  was  the  cost  per 
bushel? 

3.  In  selling  a  carriage  for  $75  a  merchant  lost  25%  on  the 
cost.     What  was  the  asking  price  if  the  carriage  was  marked 
to  gain  25  %  ? 

4.  A  newsboy  sold  92  papers  on  Tuesday.     If  this  number 
was  23J%  less  than  the  number  sold  on  Monday,  how  many 
papers  were  sold  on  the  two  days  ? 

5.  A  dealer  sold  a  quantity  of  apples  at  $6  per  barrel,  and 
by  so  doing  lost  16|-%.     If  he  paid  $309.60  for  the  apples, 
how  many  barrels  did  he  buy  ? 

6.  After  paying  174.35  for  mileage,  132.50  for  hotel  bills, 
and  $13.15  for    sundry  items,  a   traveler   finds   that   he   has 
expended  40%  of  his  money.     How  much  had  he  at  first? 

ORAL   REVIEW  EXERCISE 

1.    By  inspection  find  12| %  of  the  following  numbers  : 


a.  $872. 
b.  648  bu. 
c.  1264  A. 
d.  960  mi. 

e.  $2464. 
/.  2696  A. 
g.  1624  ft. 
h.  1832  mi. 

i.  $1688. 
j.  2072  A. 
k.  11,464  mi. 

1.  37,128  mi. 

m.  $24.72. 
n.  $168.48. 
o.  $176.24. 

p.  $2184,32. 

2.    By  inspection  find  10 
25%;  125%;   20%. 


of  each  of  the  above  numbers  ; 


JQ    ,     .LUU  yfl    ,     ^v  y0. 

\.    State  the  missing  term  in  each  of  the  following : 


K 

a. 

1600 

7*% 

? 

/• 

966 

16|  % 

? 

b. 

$650 

v 

|39 

9- 

? 

8i% 

15  bu. 

c. 

? 

4% 

$18 

h. 

1275 

65  % 

9 

d. 

900 

9 

720 

i. 

9 

<H% 

21  mi. 

e. 

? 

4% 

20 

J- 

400 

V 

600 

PERCENTAGE  237 

4.  By  inspection  find  10  %  of  each  of  the  following  : 

a.  1264.  d.  $840.  g.  $232.  /.  12448. 

b.  $920.  e.    1750.  h.  $144.  &.  $1432. 

c.  $720.  /.   $364.  i.    $288.  I.   $3624. 

5.  By  inspection  find  1^  %  of  each  of  the  above  numbers  ; 
1|%  ;   1000%  ;   125%;   166f%. 

6.  By  inspection  find  the  numbers  of  which 

a.  101  is  81%.  d.  75  is  25%.  g.    960  is  320%. 

b.  150isl6|%.  e.    125  is  20%.  h.    1920  is  32%. 

c.  170  is  331%.  /.    750  is  250%.  i.    240  is  33J%. 

WRITTEN  REVIEW  EXERCISE 

1.  A  collector  charged  4%  on  all  amounts  collected.     If  he 
remitted  to  his  customers  in  one  month  $3720.48,  how  much 
did  he  receive  for  his  services? 

2.  A  father    left  to  his  son  60  %  of  his    estate  and  to  his 
daughter  the  remainder,  $9390.88.     What  was  the  value  of  the 
estate  and  how  much  did  the  son  receive? 

3.  A  farmer  planted  1  bu.  3  pk.  of  oats  on  an  acre  of  ground 
and  harvested  56  bu.     What  per    cent  of  the  yield  was  the 
planting?     What  per  cent  of  the  planting  was  the  yield? 

4.  A  merchant  paid  the  following  charges  on  a  bill  of  goods  : 
cartage  $12.45,  freight  $65.32,  insurance  $41.     If  the  charges 
represent  5  %  of  the  face  of  the  bill,  what  was  the  gross  cost  of 
the  goods? 

5.  A  merchant  failed  in  business,  his  resources  amounting 
to  $12,840  and  his  liabilities  to  $24,000.     What  per  cent  of  his 
indebtedness  did  he  pay,  and  what  was  the  aggregate  loss  to 
his  creditors  ? 

6.  The  density  of  population  in  Asia  is  approximately  125 
per  square  mile,  and  in  the  United  States,  approximately  25  per 
square  mile.     What  per  cent  greater  is  the  density  of  popula- 
tion in  Asia  than  that  in  the  United  States?     What  per  cent 
less  is  the  density  in  population  in  the  United  States  than  that 
in  Asia? 


238  PRACTICAL   BUSINESS   ARITHMETIC 

7.  A  man  had  6  A.  of  land ;  to  one  party  he  sold  a  piece 
25  rd.  by  20  rd.,  and  to  another  party  140  sq.  rd.     What  per 
cent  of  the  field  remained  unsold? 

8.  In  a  recent  year  176,774,300  Ib.  of  fish  were  landed  in 
Boston,  and  of  this  quantity  Gloucester  furnished  111,367,809 
Ib.     What  per  cent  was  furnished  by  Gloucester  ?     (Correct  to 
the  nearest  .01.) 

9.  A  owned  property  valued  at  $12,000  from  which  he 
received  a  yearl}7  rental  of  I960.     If  he  paid  taxes  amounting 
to  8160,  insurance  $75.50,  and  made   repairs   amounting   to 
$  184. 50,  what  per  cent  net  income  did  he  receive? 

10.  B  owns  a  field  80  rd.  square.     During  a  certain  year 
this  field  yielded  on  an  average  25  bu.  of  wheat  to  an  acre. 
The  wheat  when  sold  at  $1  a  bushel  produced  an  amount  equal 
to  25  %  of  the  value  of  the  field.     What  was  the  value  of  the 
field? 

11.  A    landowner  rented  a  field  to   a   tenant  and  was   to 
receive  as  rent  16J  %  of  the  grain  raised.     The  owner  of  the 
field  sold  his  share  of  the  grain  for  84^  per  bushel,  receiving 
$  298.20.     If  the  tenant  sold  his  share  of  the  grain  for  the  same 
price  per  bushel,  how  much  did  he  receive  ? 

12.  Twenty  years  ago  the  value  of  knit  goods  produced  in 
the  United  States  was  139,271,900,  of  which   New   England 
produced  27  %  ;  the  value  of  the  knit  goods  manufactured  this 
year  was  $101,337,000,  of  which  New  England  produced  18%. 
What   was   New  England's   per   cent  of   increase   in  20  yr.  ? 
(Correct  to  the  nearest  .01.) 

13.  By  a  recent  census  report  it  was  shown  that  the  value 
of   all   personal    property    in    the    state    of    New    York    was 
approximately  $  500,000,000  and  the  value  of  all  the  real  estate 
approximately   13,000,000,000.      Draw   parallel   lines   making 
a  comparison  of  personal  property  and  real  estate.     The  real 
estate  is  what  per  cent  greater  than  the  personal  property  ? 
The   personal   property  is  what  per  cent  less  than  the   real 
estate  ? 


PERCENTAGE  239 

14.  A  young  man  entered  a  bank  as  cashier  and  at  the  end 
of  the  first  year  his  salary  was  increased  25%  ;  at  the  end  of 
the  second  year  he  was  given  an  increase  of  20  %  ;  and  at  the 
end  of  the  third  year  he  was  given  an  increase  of  25  %,  which 
made  his  salary  $  4500.     What  salary  did  he  receive  at  first  ? 

15.  A  government  statistician  collected  facts  regarding  wages 
and  income  from  nearly  two  thousand  private  manufacturing 
concerns,  and  reported  the  following :  the  average  wages  of  all 
employees,  men,  women,  and  children,  per  year  was  1263.06,  and 
the  average  net  profit  for  each  employer  was  $  2273.     What  per 
cent  greater  was  the  income  of  each  employer  than  of  each  em- 
employee  ?     (Correct  to  the  nearest  .01.) 

(Q—         |       .    .""FT      i . i .  i .  i .  i  ~?     16-   Tne  population  of  three 

liiilinlililihlilililililililil  cities  during  a  certain  year  is 

A^M^M"^"^""^"^^"""         illustrated  by  the  accompany - 

Bi^""^^"^^"^^"^"^  ing  lines,  which  are  drawn  on 

iMHMHVHMnEsnraaH  a  scale  of  12,500  inhabitants 

to  each  -J-  of  an  inch.     What  is  the  population  of  A,  B,  and  C, 

respectively  ?     The  population  of  each  city  is  what  per  cent  of 

the  population  of  the  three  cities  ? 

17.    The  annual  coal  production  in  the  United  States,  Great 
Britain,  Germany,  and  France 


for  a  certain  year  is  illustrated  l°i  I  i  I  i  I  i  I  i  1 1  I  i  1 1  h  I  i  1 1 1  1 1 1 1  i  I  1 1  i 


in  the  accompanying  rectan-  united  states 
gles,  drawn   on  the   scale    of 
20,000,000  short  tons  to  each 
-|   of  an  inch.      During  that 
year,  how  many  tons    did  the   p,.ance 
United  States,  Great  Britain,   •"• 

Germany,  and  France,  respectively,  produce  ?  The  produc- 
tion of  each  country  is  what  per  cent  of  the  production  of  the 
four  countries  ?  In  the  same  year  the  rest  of  the  world  pro- 
duced approximately  110,000,000  short  tons.  Illustrate  graph- 
ically the  world's  coal  production  for  this  year.  What  was  the 
world's  approximate  production  this  year? 


240  PRACTICAL  BUSINESS  ARITHMETIC 

18.  The  total  value  of  the  cotton  crop  to  farmers  in  a  recent 
year  was  $453,000,000  and  the  value  of  the  cotton  exported  to 
England  in  the  same  year  was  1124,000,000.     What  per  cent 
was  exported  to  England?     (Correct  to  the  nearest  .01.) 

19.  A  saleswoman  in  a  city  store  receives  $  9  per  week.     She 
pays  $3.50  per  week  for  board  and  room,  10^  per  day  for  car 
fare  6  da.  in  the  week,  20^  per  day  for  6  da.  of  each  week 
for  luncheon,  and  has  incidental  expenses  amounting  to  $  1.70. 
If  she  saves  the  remainder,  what  per  cent  of  her  weekly  wages 
does  she  save  ?     What  per  cent  does  she  spend  ? 

20.  The  production,  in  bushels,  of  grain  in  the  United  States 
in  two  recent  years  was  approximately  as  follows  : 


CEREALS 

1903 

1904 

Corn 

2,240,000,000 

2,470,000,000 

Wheat 

640,000,000 

550,000,000 

Oats 

780,000,000 

900,000,000 

Barley 

131,000,000 

130,000,000 

Rye 

30,000,000 

27,000,000 

Buckwheat 

14,000,000 

15,000,000 

Find  the  per  cent  of  increase  or  decrease  of  each  cereal  for 
1904  as  compared  with  the  previous  year.  Then  draw  a  series  of 
parallel  rectangles  to  compare  the  production  of  1904  with  the 
production  of  1903.  Also  draw  a  series  of  rectangles  to  com- 
pare the  production  of  1904  with  the  production  of  a  later  year. 

SUGGESTION.  This  may  be  represented  by  one  series  of  rectangles. 
Each  rectangle  may  be  divided  into  two  parts  —  one  shaded  and  the  other 
unshaded.  The  shaded  part  may  be  made  to  represent  the  yield  for  1904 
and  the  unshaded  part  the  yield  for  1903. 

21.  The  silver  produced  by  the  leading  sources  in  a  recent 
year  was  approximately  as  follows  : 

Mexico                        60,000,000  oz.  Canada  4,500,000  oz. 

United  States              55,500,000  oz.  Peru  4,000,000  oz. 

Bolivia                         13,000,000  oz.  Spain  3,500,000  oz. 

Australasia                   8,000,000  oz.  Chili  3,500,000  oz. 

Germany                       6,000,000  oz.  Austria-Hungary  2,000,000  oz. 

Draw  a  set  of  parallel  rectangles  to  graphically  represent  the 
above  numbers. 


PERCENTAGE 


241 


22.  In  the  following  table  is  shown  the  population  in  the 
United  States  in  a  certain  year,  at  least  ten  years  of  age,  en- 
gaged in  gainful  occupations,  classified  by  sexes  and  kinds  of 
occupations.  Supply  the  missing  terms.  Check  the  work. 


KIND  or  OCCUPATION 

POPULATION  ENGAGED  IN  GAINFUL  OCCUPATIONS 

NUMBER 

PER  CENT  OF  TOTAL 

Total 

Male 

Female 

Total 

Male 

Female 
18.4 

Agricultural  pursuits      .     .     . 
Professional  services  .... 
Domestic  and  personal  service 
Trade  and  transportation     .     . 
Manufacturing  and  mechanical 
pursuits 

10,381,765 
1,258,739 
5,580,657 
4,766,964 

7,085,992 

9,404,429 
828,163 
3,485,208 
4,263,617 

5,772,788 

977,336 
430,576 
2,095,449 
503,347 

1,313,204 

35.7 

39.6 

All  occupations   .     .     . 







100.0 

100.0 

100.0 

Public 


23.  Suppose  the  accompanying  diagram  illustrates  the  dis- 
tribution of  school  enrollment  in  the 

public,  private,  and  parochial  schools 
of  the  United  States  during  a  certain 
year.  The  private  and  parochial 
schools  are  what  per  cent  of  the 
public  schools  ?  of  the  entire  school 
enrollment  ?  The  public  schools 
are  what  per  cent  of  the  total  en- 
rollment ?  of  the  private  and  paro- 
chial schools  combined  ? 

24.  The  gold  production,  in  ounces,  in  the  eight  principal 
gold-producing  states  in  the  United  States  in  a  recent  year  was 
approximately   as    follows :     Colorado,  28,500,000 ;   California, 
17,000,000;  Alaska,  8,500,000;    Arizona,  4,000,000;  Montana, 
4,500,000;  Nevada,  3,000,000  ;  South  Dakota,  7,000,000 ;   Utah, 
3,500,000.      Compare    these   values   by   drawing   a   series    of 
parallel  rectangles. 


Parochial 


Private 


CHAPTER   XVIII 

COMMERCIAL  DISCOUNTS 
ORAL  EXERCISE 

1.  A  set  of  Scott's  works  is  marked  1 12.     If  I  buy  it  at  this 
price,  less  16f%,  what  does  it  cost  me? 

2.  I  buy  190  worth  of  goods  on  30  da.  time,  or  5%  off  for 
cash.     What  cash  payment  will  settle  the  bill  ? 

3.  I  owe  B  1600,  due  in  80  da.     He  offers  to  allow  me  5% 
discount  if  I  pay  cash  to-day.     I  accept  his  offer  and  give  him 
a  check  for  the  amount.     What  was  the  amount  of  the  check  ? 

305.  A  reduction  from  the  catalogue  (list)  price  of  an  article, 
from  the  amount  of  a  bill  of  merchandise,  or  from  the  amount 
of  a  debt,  is  called  a  commercial  or  trade  discount. 

Business  houses  usually  announce  their  terms  upon  their  bill  heads.  The 
space  allowed  for  recording  the  terms  is  usually  limited,  and  bookkeepers 
find  it  necessary  to  use  symbols  and  abbreviations  to  indicate  them.  Thus, 
if  a  bill  is  due  in  30  da.  without  discount,  the  terms  may  be  written 
N/3o,  or  Net  30  da. ;  if  the  bill  is  due  in  30  da.  without  discount,  but  an 
allowance  of  2%  is  made  for  payment  within  10  da.,  the  terms  may  be 
written  2/io,  Vso,  or  2  %  10  da.,  net  30  da. 

306.  Manufacturers,  jobbers,  and  wholesale  dealers  usually 
have  printed  price  lists  for  their  goods.     To  -obviate  the  neces- 
sity of  issuing  a  new  catalogue  every  time  the  market  changes, 
these  lists  are  frequently  printed  higher  than  the  actual  selling 
price  of  the  goods,  and  made  subject  to  a  trade  discount. 

307.  The  fluctuations  of  the  market  and  the  differences  in 
the  quantities  purchased  by  different  customers  frequently  give 
rise  to  two  or  more  discounts  called  a  discount  series. 

Large  purchasers  sometimes  get  better  prices  and  terms  than  small  pur- 
chasers. Thus,  the  average  customer  might  be  quoted  the  regular  prices 
less  a  trade  discount  of  25%,  while  an  especially  large  buyer  might  be  quoted 
the  regular  prices  less  trade  discounts  of  25  %  and  10  %. 

242 


COMMERCIAL   DISCOUNTS  243 

308.  When  two  or  more  discounts  are  quoted,  one  denotes  a 
discount  off  the  list  price,  another,  a  discount  off  the  remainder, 
and  so  on. 

The  order  in  which  the  discounts  of  any  series  is  considered  is  not 
material.  Thus,  a  series  of  25  %,  20  %,  and  10  %  is  the  same  as  one  of  20  %, 
10  %,  and  25  %,  or  one  of  10  %,  25  %,  and  20  %. 

309.  Catalogue  prices  are  generally  estimated  on  the  basis  of 
credit  sales,  and  a  cash  purchaser  is  given  the  usual  trade  dis- 
count and  a  special  discount  for  early  payment.     This  latter 
discount  has  the  effect  of  encouraging  prompt  payments. 

The  list  price  is  sometimes  called  the  gross  price  and  the  price  after  the 
discount  has  been  deducted  the  net  price. 

FINDING   THE   NET   PKICE 

310.  Example.    The  list  price  of  a  dozen  pairs  of  shoes  is 
145.     If  this  price  is  subject  to  a  discount  series  of  20%  and 
10  %,  what  is  the  net  selling  price  ? 

SOLUTION.    20%  or  ^  of  $45  =  $9,  the  first  discount. 

$45  _  $9  —  $36,  the  price  after  the  first  discount. 
10%  or  TV  of  $36  =  $3.60,  the  second  discount. 
$36  -  $3.60  =  $32.40,  the  net  selling  price. 

ORAL  EXERCISE 
Find  the  net  price  : 


LIST 

TRADE 

LIST 

TRADE 

LIST 

TRADE 

PRICE 

DISCOUNT 

PRICE 

DISCOUNT 

PRICE 

DISCOUNTS 

1 

.  $4 

25% 

8.  $6 

40% 

15. 

$4 

25% 

and 

331% 

2 

.  $15 

20% 

9.  $4       12|  % 

16. 

$30 

331^ 

?o  and 

25% 

3 

.   $90 

331% 

10.   $24     81% 

17. 

$35 

20% 

and 

25% 

4 

.   $20 

10% 

11.   $42 

16f% 

18. 

$45 

20% 

and 

16f  % 

5 

.   $50 

50% 

12. 

$35 

20% 

19. 

$50 

20% 

and 

25% 

6 

.   $2.50 

20% 

13. 

$100 

25% 

20. 

$100 

20% 

and 

10% 

7 

.   $4.50 

16f  % 

14. 

$720 

33J% 

21. 

$600 

16|9 

o  and 

20% 

22.  A  piano  listed  at  $750  is  sold  less  331  %,  20  %,  and  10  %. 
What  is  the  net  cost  to  the  purchaser  ? 

23.  A  dealer  offers  cloth  at  $3.50  per  yard  subject  to  a  dis- 
count of  20  %.     How  many  yards  can  be  bought  for  $56  ? 


244 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 

Find  the  net  price  : 

GROSS  GROSS 

SELLING  PRICE  TRADE  DISCOUNTS     SELLING  PRICE  TRADE  DISCOUNTS 

1.  $3360     25%  and  10%       4.   $2500     20%,  10%,  and  5% 

2.  $3510     331%  and  20%     5.   $5400     25%,  20%,  and  10% 

3.  $4500     20%andl6|%     6.   $3960     331%,  20%,  and!6f  % 

7.  The  list  price  of  cloth  is  $4.80  per  yard,  but  this  price  is 
subject  to  discounts  of  25%  and  20%.     How  many  yards  can 
be  bought  for  $288? 

8.  A  hardware  dealer  sold  25  doz.  5-in.  files  at  $2.50  and 
25  doz.  12-in.  files  at  $7.50,  less  50%  and  10%  ;   150  machine 
bolts  at  $21.50  per  C,  less  20%  and  10%.     What  was  the  net 
amount  of  the  bill  ? 

9.  Study    the    following   model.       Copy   and   find   the    net 
amount  of  the  bill,  using  the  discounts  named  in  the  bill,  and 
the  following  prices  :  5-in.  pipe,  $1.45  ;  1-in.  pipe,  17^  ;  valves, 
$2.67. 


Bought  of  GEORGE  W.  MUNSON  &  CO. 

Terms  £  rt^^z 


2,0 


Z2L 


22- 


COMMERCIAL  DISCOUNTS  245 

10.  One  firm  offers  a  piano  for  $400,  subject  to  discounts  of 
and  20  %  ;   another  offers  the  same  piano  for  $  400  less 

discounts  of  25  %  and  15%.     Which  is  the  better  offer?     How 
much  better? 

11.  A  jobber  bought  a  quantity  of  goods  listed  at  $ 3600,  sub- 
ject to  discounts  of  25%  and  20%.     He  sold  the  goods  at  the 
same  list  price,  subject  to  discounts  of  20  %  and  10  %.     Did  he 
gain  or  lose,  and  how  much? 

12.  Make  out  bills  for  the  following,  using  the  current  date 
and   the  name  and  address  of   some  dealer  whom  you  know. 
Terms  in  each  case,  60  da.  net. 

a.  You  bought  12  doz.  hand  saws,  #27,  at  118.50;  7J  doz. 
mortise  locks,  #271,  at  $4.25;  25  doz.  pocket  knives,  #27,  a£ 
$7.50;  and  If  doz.  cheese  knives  at  $8. 25.    Discount:  25  fo,  10/o. 

b.  You  bought  41 J'  of  2"  extra  strong  iron  pipe  at  70^; 
941'  of  1|"  extra  strong  iron  pipe  at  31 J-^;   153J'  of  \"  iron 
pipe  at  6J7;  88|'  of  f"  iron  pipe  at  7££     Discount:  25$fe,  lOflb. 

c.  You  bought  25  kitchen  tables  at  $3.25;  25  dining-roorn 
tables   at  $8.75;    15  doz.   dining-room   chairs  at  $12.50;    12 
antique  rockers  at  $12.25;  and  15  oak  bedroom  sets  at  $32.50. 
Discount:  16f  %,  5%. 


FINDING  A  SINGLE  EATE  OE  DISCOUNT  EQUIVALENT 
TO   A   DISCOUNT   SERIES 

311.    Example.    What  single  rate  of  discount  is  equivalent 
to  a  discount  series  of  25  %,  331  %?  alld  10  %  ? 

SOLUTION.     Represent   the    list   price    by  1.00 

100%.    Then,  75%  equals  the  price  after  the  25  (25%  of  100  %) 

first  discount,  50%  the  price  after  the  second  __ 
discount,  and  45%  equals  the  net  selling  price. 

100%,  the  list  price,  minus  45%,  the  net  selling  -25  (33J  %  of  75  %) 

price,  equals  55%,  the  single  rate  of  discount  .50 

equivalent  to  the  given  discount  series.  Q/J  /^Q  <^    of  50  %^) 

A  single  discount  equivalent  to  a  discount  . 
series  may  often  be  determined  mentally  (see 

§§  312-313).  100  %  -  45  %  =  55  % 


246  PRACTICAL   BUSINESS   AE1THMETIC 

WRITTEN  EXERCISE 

1.  Find  a  single  rate  of  discount  equivalent  to  a  discount 
series  of  50%,  25%,  20%,  and  10%. 

2.  Which  is  the  better  and  how  much,  a  single  discount  of 
65  %  or  a  discount  series  of  25  %,  20  %,  and  20  %  ? 

3.  The  net  amount  of  a  bill  of  goods  was  $  450  and  the  dis- 
counts  allowed  were  25%,  33^%,  and  10  %.     Find  the  total 
discount  allowed. 

4.  I  allowed  a  customer  discounts  of  50%,  10  %,  and  10  % 
from  a  list  price.     What  per  cent  better  would  a  single  dis- 
count of  65  %  have  been  ? 

5.  Goods  were  sold  subject  to  trade  discounts  of  25  %,  20  %, 
and  10  %.     If  the  total  discount  allowed  was  $460,  what  was 
the  net  selling  price  of  the  goods  ? 

6.  A  quantity  of  goods  was  sold  subject  to  trade  discounts 
of  20  %  and  20  %.     The  terms  were  60  da.  net  or  5  %  off  for 
payment  within  10  da.     If  a  cash  payment  of  i  1026  was  re- 
quired 3  da.  after  the  date  of  the  bill,  what  was  the  list  price 
of  the  goods  sold  ? 

312.  Since  the  first  of  a  series  of  discounts  is  computed  on 
100  %  of  the  list  price,  and  the  second  on  100  %  minus  the  first 
discount,  it  follows  that  the  sum  of  any  two  separate  discounts 
exceeds  the  equivalent  single  discount  by  the  product  of  the  two 
rates  per  cent. 

Thus,  in  a  discount  series  of  20%  and  20%  the  apparent  single  discount  is 
the  sum  of  the  two  separate  discounts  or  40%;  but  since  the  second  discount 
is  not  computed  on  100%,  but  on  80%,  40%  exceeds  the  true  single  discount 
by  20  %  of  20  %,  or  4% ;  and  the  equivalent  single  discount  is  40  %  minus  4  %, 
or  36  %.  Hence, 

313.  To  find  the  single  discount  equivalent  to   a  series  of 
two  discounts : 

From  the  sum  of  the  separate  discounts  subtract  their  product, 
and  the  remainder  ivill  be  the  equivalent  single  discount. 

When  two  separate  discounts  cannot  be  reduced  to  a  single  discount 
mentally,  proceed  as  in  §  311 ;  when  they  can,  proceed  as  in  §  313. 


COMMERCIAL   DISCOUNTS  247 

ORAL    EXERCISE 

State  a  single  rate  of  discount  equivalent  to  a  discount  series  of: 

1.  10%  and  10%.  17.  50%  and  5%.  33.  25%  and  8%. 

2.  20%  and  20%.  18.  10%  and  5%.  34.  8J%  and  24%. 

3.  30%  and  30%.  19.  20%  and  5%.  35.  8^%  and  36%. 

4.  40%  and  40%.  20.  40%  and  5%.  36.  35%  and  10%. 

5.  50%  and  50%.  21.  25%  and  30%.  37.  20%andl2|%. 

6.  20%  and  10%.  22.  25%  and  40%.  -38.  40%  and  121%. 

7.  30%  and  10%.  23.  20%  and  15%.  39.  60%andl2|%. 

8.  40%  and  10%.  24.  40%  and  15%.  40.  12%  and  121%. 

9.  50%  and  10%.  25.  35%  and  20%.  41.  24%andl6f%. 

10.  60%  and  10%.  26.  45%  and  20%.  42.  16|%and20%. 

11.  30%  and  20%.  27.  55%  and  20%.  43.  14f%and35%. 

12.  40%  and  20%.  28.  60%  and  25%.  44.  16|%and25%. 
13..  50%  and  20%.  29.  40%  and  25%.  45.  33^%  and  15%. 

14.  60%  and  20%.      30.    60%  and  20%.        46.    66f%andl5%. 

15.  25%  and  10%.      31.    25%  and  33^%.      47.    11|%  and  18%. 

16.  35%  and  10%.      32.    45%  and  331%.      48,   36%  and  111%. 

314.  When  a  discount  series  consists  of  three  separate  rates, 
the  first  two  may  be  combined  as  in  §  313  and  then  the  result 
and  the  third  may  be  combined  in  the  same  manner. 

315.  Example.     Find    a    single  rate  of  discount  equivalent 
to  a  discount  series  of  25%,  20%,  and  20%. 

SOLUTION.  — Combine  the  first  two  by  thinking  25%  +  20%-  5%  =  40%,  the 
single  discount  equivalent  to  the  series  25%  and  20%.  20%  +  40  %  —  8%  =  52%, 
or  the  single  rate  equivalent  to  the  discount  series  25%,  20%,  and  20%. 

ORAL  EXERCISE 

State  a  single  rate  of  discount  equivalent  to  a  discount  series  of: 

1.  20%,  25%,  and  20%.  7.  20  %,  10%,  and  10%. 

2.  20%,  15%,  and  10%.  8.  40  %,  10%,  and  10%. 

3.  20%,  20%,  and  20%.  9.  50%,  10  %,  and  10%. 

4.  10%,  10%,  and  10%.  10.  30  %,  10%,  and  10%. 

5.  20%,  20%,  and  10%.  11.  20  %,  25%,  and  10%. 

6.  25%,  33J%,  and  10%.  12.  20%,  20  %,  and  25%. 


248  PRACTICAL   BUSINESS   ARITHMETIC 

316.  When  it  is  not  desirable  to  show  the  separate  discounts, 
the  net  selling  price  may  be  found  as  shown  in  the  following 
example. 

317.  Example.     A   mahogany  sideboard   listed   at  1175   is 
sold  subject  to  trade  discounts  of  20%  and  25%.     Find  the 
net  cost  to  the  purchaser. 

SOLUTION.  By  inspection  determine  that  a  100  %  —  40  %  =  60  % 
discount  of  40%  is  equivalent  to  a  series  of  25%  ^Q  ^  Q£  JM  75  _  $105 
and  20%.  Represent  the  gross  cost  by  100%. 

Then  100%  —  40%  —  60%,  the  net  cost  to  the  purchaser;  that  is,  the  net  cost 
of  the  sideboard  is  60%  of  the  list  price.  60%  of  $  175  =  $  105,  the  net  cost  to 
the  purchaser. 

ORAL  EXERCISE 

By  inspection  find  the  net  cost  of  articles  listed  at: 

1.  1400,  less  20%  and  25%.     5.    $1000,  less  50  %  and  50%. 

2.  8300,  less  20%  and  20%.     6.    $1000,  less  30%  and  10%. 

3.  $600,  less  10%  and  10%.     7.    $200,  less  60%  and  25%. 

4.  $200,  less  30%  and  30%.     8.    $400,  less  20%  and  40%. 

WRITTEN  EXERCISE 

1.  Find  the  net  selling  price  of  a  piano  listed  at  $450,  less 
20%  and  20%. 

2.  Find  the  net  selling  price  of  an  oak  sideboard  listed  at 
$125,  less  25%,  33J%,  and  10%. 

3.  I  bought  125  cultivators  listed  at  $8.50,  each  subject  to 
trade  discounts  of  20%  and  25%.     If  I  paid  freight  $30.50 
and  drayage  $7.90,  how  much  did  the  cultivators  cost  me? 

4.  The  net  cost  of  an  article  was  increased  $30  by  freight, 
making  the  actual  cost  of  it  $630.     What  was  the  list  price  of 
the  article,  the  rates  of  discount  being  25  %  and  33^%  ? 

5.  You  desire   to   buy   24,000   ft.   choice  cypress :   one   firm 
quotes  you  $60  per  thousand  feet,  less  trade  discounts  of  20  % 
and  5%  ;  another  firm  offers  you  the  same  lumber  at  $75  per 
thousand  feet,  less  33J%  and  8%.     The  terms  offered  by  both 
firms  are  1/10,  N/3o-      You  accept  the  better  offer  and  pay  cash. 
How  much  does  the  lumber  cost  you? 


COMMERCIAL   DISCOUNTS 


249 


WRITTEN   REVIEW   EXERCISE 

1.  Find  the  cost  of  125  1-J-"  brass  ells  at  11.25  each,  less 
20  Jfe,  and  10  J6. 

2.  An  agent  bought  10  pianos  listed  at  1450  each,  less 

and  10%,  and  sold  them  for  1400  each,  less  10  %  and  5%.    Did 
he  gain  or  lose  and  how  much? 

3.  Apr.  15,  E.  L.  Gano  bought  of  W.  L.  Cunningham  &  Co. 
5  phaetons   listed  at  $450  each,  less  25%  and  20%.     Terms: 
2/30i  Veo-     How  much  ready  money  would  settle  the  bill? 

4.  Study  the  following  bill.     Copy  and  find  the  net  amount 
of  it,  using  the  discounts  indicated  in  the  bill,  and  the  follow- 
ing prices:   windmills,   1675;   pumps,  $610;    1-in.   iron   pipe, 
17J^;  4-in.  iron  pipe,   73^;   hose,  97^;   elbows,  21^;  valves, 
$1.49. 


Terms 


Bought  of  E.  M.  MCGREGOR  &  co. 

y/*.  '/j,.  *s< 


?/?  /  &  a 


^^  ^1 


2-Q 


/?2- 


IJtf 


/JJ 


250  PRACTICAL   BUSINESS    ARITHMETIC 

5.  How  much  cash  would  settle  the  model  bill  (page  249) 
Oct.  30?   Nov.  8?     How  much  cash  would  settle  the  bill  called 
for  in  problem  4,  if  it  is  paid  for  on  the  day  it  is  written?     If 
it  is  paid  Nov.  15?     Copy  the  model  bill  in  the  form  that  it 
would  be  written  if  cash  accompanied  the  order ;  that  is,  copy  it 
deducting  the  3  %  allowed  for  immediate  payment. 

6.  Copy  and  find  the  net  amount  of  the  following  bill : 

Leith,  Scotland,          May  10,    19 

Invoice  of  Wire  Cloth 
Shipped  by  the  J.    M.    ROBERTS  COMPANY 

In  the  Steamship  Winifredian    To  Edward  M.  Davidson  &  Co. 

Philadelphia,  Pa. 


6  pc.,  each  34'  x  51  6"  1122  sq.  ft.  1/3  70   2  6 

6   "     •   40'  x  6'  6"   ****        1/4  ***«,  *  * 
6   "     "   42'  x  7-  4"   ****        1/5  ***  **  * 

3   "     "   48'  x  7'  2"   ****        1/5   **  **  * 

***  **  * 

Less  10%  **  **  *  ***  **  * 

7.  E.   M.   French  &  Co.,  Albany,  N.Y.,  bought  of  Austin 
Bailey  &  Co.,  Boston,  Mass.,  Apr.  12,  3  doz.  pr.  hinges,  8  in.,  at 
$4.20,  and  3  doz.  pr.  hinges,  4  in.,  at  $2.10,  less  60%,  10%, 
and  10%  ;   50  Ib.  brads,  f  in.,  at  90^,  and   50  Ib.  brads,  f   in., 
at   80^,   less   50%,   10%,    and   5%.     Terms:  2/10,  N/3o-     Find 
the  net  amount  of  the  bill  Apr.  15. 

8.  D.    M.    DeLong,   Portland,   Me.,    sold    S.    H.    Shapleigh 
&  Co.,  Concord,  N.H.,  on  account  30  da.,  2%  10  da.:   35  cul- 
tivators listed  at  $7.50  each,  less  20%  and  10%  ;  15  doz.  table 
knives  listed  at  $9.75,  less  10%  ;   15  doz.  hair  curlers  at  90^, 
less  5%  ;  15  doz.  locks,  No.  534,  at  $3.75,  less  10%  and  5%  ; 
|  doz.  steel  squares,  No.  8,  at  $36,  less  25%  and  10%  ;  ^  gro. 
knives  and  forks,  No.  760,  at  $12,  less  20%  and  10%  ;  f  doz. 
cheese  knives  at  $9.75,  less  16|%.     Find  the  net  amount  of 
the  bill  5  da.  after  date. 


COMMERCIAL  DISCOUNTS 


251 


9.    Aug.  5,  you  buy  of  Gray,  Salisbury  &  Son,  New  York 
City,  4000  Ib.  raisins  at  16 £  less  trade  discounts  of  25%,  20%, 
and  10%.     Terms:  2/10,  N/so-      You  pay  cash  for  freight  13.20. 
If  you  pay  the  bill  Aug.  7,  what  will  the  raisins  cost  you? 
10.    Find  the  net  amount  of  the  following  bill : 


Jan.  5, 


W.  H.  Meachum 

Springfield,  Mass. 


Ceonarcl,  ffi,oss  <$•  Go.,  =£)/». 


*/e/*/ns  Net   60  da. 


1/2  C  Machine  Bolts    3/8  x  1  1/2"   $2.40 
1/2  C                      3"        2.88 
1/2  C                      6  1/2"    4.00 
1/2  C                 1/2x3  1/2"     4.64 
1/2  C                       5"         5.42 
1/2  C                      6"        5.94 
1/2  C                      9"        7.50 
1/2  C                      10"        8.02 
1/2  C                 5/8  x  4"         7.10 
1/4  C                      4  1/2"     7.48 
1/4  C                3/4  x  5"       10.70 
1/4  C                      10"        15.70 
1/4  C                     16"       21.70 

Discounts:  5056,  1056.  556 
5   doz.   Files             5"       $2.50 
5                         6"        3.10 
2                         12"        7.50 
3                         4"3.00 
2                         5"        3.20 
1                         10"        7.40 
1/2                       12"       10.20 
Discounts:  50%,  10%.  5%,  556 

11.  You  desire  to  buy  200  Ib.  nutmeg.  You  find  that  S.  S. 
Pierce  Co.,  of  your  city,  offer  this  article  at  75^  per  Ib.,  less  a 
discount  of  25%,  and  that  Smith,  Perkins  &  Co.,  New  York 
City,  offer  it  at  70^  per  Ib.,  less  discounts  of  15%  and  10%. 
The  freight  from  New  York  to  your  city  on  a  package  of  this 
kind  is  $1.50.  The  terms  offered  by  both  firms  are:  yio,  N/30. 
You  accept  the  better  offer  and  pay  cash.  How  much  does 
the  nutmeg  cost  you? 


CHAPTER   XIX 

GAIN  AND  LOSS 
ORAL  EXERCISE 

1.  What  is  33^%  of  $660?     How  much  is  gained  on  goods 
bought  for  8900  and  sold  at  a  profit  of  331%  ? 

2.  What  per  cent  greater  is  175  than  $60?  what  per  cent 
less  is  $60  than  $75?      Goods  bought  for  $100  are  sold  for 
$150.     What  is  the  gain  per  cent? 

3.  What  per  cent  less  is  $80  than   $100?  what   per   cent 
more  is  $100  than  $80?     Goods  bought  for  $100  are  sold  for 
$90.     What  is  the  loss  per  cent  ? 

4.  If  $800  is  increased  by  25%  of  itself,  what  is  the  result? 
Goods  bought  for  $1400  are  sold  at  a  profit  of  25%.     What  is 
the  selling  price  ? 

5.  If  $1500    is   decreased  by   331%   Of  itself,   what  is  the 
result?     Goods  bought  for  $2700  are  sold  at  a  loss  of  331%. 
What  is  the  selling  price  ? 

6.  State  a  brief  method  for  finding  a  gain  of  6^%;  a  gain 
of  6|%;  a  gain  of  81% ;   a  gain  of  10% ;  a  gain  of  \\% ;   a  gain 
of  lf%;  a  gain  of  2-|  %;   a  gain  of  31%. 

7.  State  a  brief  method  for  finding  a  loss  of  11  \%\  a  loss 
of  12|% ;  a  loss  of  14f  % ;  a  loss  of  16|%  ;   a  loss  of  20%  ;  a  loss 
of  25%  ;  a  loss  of  9T\  %  ;  a  loss  of  37|%. 

8.  State  a  brief  method  for  finding  a  gain  of  33J%;  a  gain 
of  22|%;  a  gain  of  50%  ;  a  gain  of  66|%;  a  gain  of  75  %. 

318.  The  gains  and  losses  resulting  from  business  transac- 
tions are  frequently  estimated  at  some  rate  per  cent  of  the  cost, 
or  of  the  money  or  capital  invested. 

Since  no  new  principles  are  involved  in  this  subject,  illustrative  examples 
are  unnecessary. 

252 


GAIN   AND   LOSS 


FINDING   THE   GAIN   OR   LOSS 


ORAL   EXERCISE 


253 


By  inspection  find  the  gain  or  loss  : 
PER  CENT                                 PER  CENT 

PER  CENT 

COST 

OF  GAIN 

COST 

OF  Loss 

COST 

OF  GAIN 

1. 

$2900 

50% 

9. 

$1500 

10% 

17. 

$7500 

20% 

2. 

$1600 

75% 

10. 

$1600 

1  ~  % 

18. 

$1400 

25% 

3. 

$5600 

284% 

11. 

$3000 

1  ^  tf 

19. 

$2200 

9^1% 

4. 

$2700 

m% 

12. 

$4800 

4% 

20. 

$8100 

1H% 

5. 

$2400 

37  1% 

13. 

$3600 

H% 

21. 

$6400 

12|% 

6. 

$1400 

42f% 

14. 

$3200 

6|% 

22. 

$2800 

14f% 

7. 

$3200 

6*^-^-  tfr\ 

15. 

$4500 

6f% 

23. 

$9600 

16^% 

8. 

$2100 

66-  tfr\ 

16. 

$8400 

8J% 

24. 

$3600 

22f% 

25-48. 

Find  the 

selling 

price 

in  each 

of  the 

above  problems. 

WRITTEN  EXERCISE 

1.  An  importation  of  silks  invoiced  at  <£40  10s.  was  sold  at 
a  profit  of  25  %  -     Find  the  amount  (in  United  States  money) 
of  the  gain. 

2.  An  importation  of  German  toys  invoiced  at  43,750  marks 
was  sold  at  a  gain  of  33J  %.    Find  the  amount  (in  United  States 
money)  of  the  gain. 

3.  An  article  that  cost  $1  was  marked  10%  above  cost.     In 
order  to  effect  a  sale,  it  was  afterward  sold  for  10  %  below  the 
marked  price.     Find  the  gain  or  loss  on  250  of  the  articles. 

4.  A  man  bought  a  city  lot  for  $1150  and  built  a  house  on 
it  costing  $2650.      He  then  sold  the  house  and  lot  at  a  gain  of 
5  %.     How  much  did  he  gain  and  what  was  his  selling  price  ? 

5.  A  man  bought  a  quantity  of  silk  for  $450,  a  quantity  of 
fancy  plaids  for  $  120,  and  a  quantity  of  velvet  for  $  90.     He 
sold  the  silk  at  a  gain  of  25%,  the  plaids  at  a  loss  of  5  %,  and 
the  velvet  at  a  gain  of  33J%.      What  was  his  gain,  and  how 
much   did   he   realize    from    the    sale  of    the    three    kinds   of 
material  ? 


254  PRACTICAL   BUSINESS   ARITHMETIC 


FINDING   THE   PER   CENT   OF   GAIN   OR   LOSS 

ORAL   EXERCISE 

By  inspection  find  the  per  cent  of  gain  or  loss  : 

COST       GAIN  COST     Loss  COST  SpJ£™°  SPR"E°  GAIN 

1.  1100    §10        7.   $60    #15     13.   $80    190     19.  1300    $60 

2.  $150    $50        8.   $40    $10     14.   $90    $80     20.  $115    $23 

3.  $140    $70        9.   $90    $45     15.   $60    $75     21.  $102    $17 

4.  $140    $140     10.   $70    $14     16.   $75    $60     22.  $420    $60 

5.  $200    $400     11.   $80    $16     17.   $10    $50     23.  $300    $200 

6.  $300    $750     12.   $15    $10     is.    $50  $10     24.  $700    $100 


WRITTEN   EXERCISE 

1.  A  milliner  bought  hats  at  $15  a  dozen  and  retailed  them 
at  $3  each.     What  per  cent  was  gained  ? 

2.  A  stationer  bought  paper  at  $2  a  ream  and  retailed  the 
same  at  a  cent  a  sheet.     What  was  his  per  cent  of  gain  ? 

3.  A  dry-goods  merchant  bought  gloves  at  $7.50  a  dozen 
pair  and  retailed  them  at  $1.25  a  pair.      What  was  his  per  cent 
of  gain  ? 

4.  A  merchant  imported  50  gro.  of  table  knives  at  a  cost 
of  $1125.     Two  months  later  he  found  that  the  sales  of  table 
knives  aggregated  $920  and  that  the  value  of  the  stock  unsold 
was  $435.     Did  he  gain  or  lose,  and  what  per  cent  ? 

5.  An  importer  bought  a  quantity  of  silk  goods  for  £  400  5s. 
After  disposing  of  a  part  of  the  goods  for  $1200  he  took  an 
account  of  the  stock  remaining  unsold  and  found  that  at  cost 
prices  it  was  worth  $1047.82.      Did  he  gain  or  lose,  and  what 
per  cent  ? 

6.  Jan.    1,  F.    E.   Smith    &  Co.   had  merchandise  on    hand 
valued    at   $2500.      During   the    month  they  purchased  goods 
costing  $6000  and  sold  goods  amounting  to   $7500.      If   the 
stock  on  hand  at  cost  prices  Feb.  5  was  worth  $2500,   what 
was  the  per  cent  of  gain  on  the  sales  ? 


GAIN   AND   LOSS  255 

FINDING   THE   COST 

ORAL  EXERCISE 

By  inspection  find  the  cost  : 

Loss      RATE  or  Loss  GAIN     RATE  OF  GAIN 

1.  $150  10%  7.  $35  20% 

2.  $100  li%  8.  $79  25% 

3.  $200  1|%  9.  112  111% 

4.  $450  2|%  10.  $19  16f% 

5.  $220  6|%  11.  $44  22|% 

6.  $115  81%  12.  $15  33i% 

SELLING          RATE  SELLING         RATE 

PRICE         OF  G.VN  PRICE         OF  Loss 

13.  $1050         5%  19.     $950         5% 

14.  $2040       2%  20.    $900       50  % 
is.    $3600       20%                               21.    $150       6|  % 

16.  $1400       16|%  22.    $550       16|% 

17.  $1800       12|%  23     |240       33_i% 
is.    $2400       33|%  24.    $500       22|  % 

25-36.    Find  the  selling  price  in  problems  1-12. 
37-48.    Find  the  gain  or  loss  in  problems  13-24. 

49.  B  sold  a  farm  %•  $2400,  thereby  losing  25  %.     For  how 
much  should  he  have  sold  it  to  have  gained  10  %  ? 

50.  By  selling  a  piano  at  $400  a  dealer  realizes  a  gain  of 
33J%.     What  would  be  the  selling  price  of  the  piano  if  sold 
at  a  gain  of  25  %  ? 

WRITTEN  EXERCISE 

1.  A  sleigh  was  sold  for  $64.80,  which  was  10  %  below  cost. 
What  was  the  cost  ? 

2.  An  office  safe  was  sold  at  $102,  which  was  20%  above 
cost.     What  was  the  cost  ? 

3.  A    merchant  marks  goods  16|  %  above  cost.      What  is 
the  cost  of  an  article  that  he  has  marked  $21.70? 


256  PRACTICAL   BUSINESS   ARITHMETIC 

4.  An  owner  of  real  estate  sold  2  city  lots  for  -112,000  each. 
On  one  he  gained  25%  and  on  the  other  he  lost  25%.     What 
was  his  net  gain  or  loss  from  the  two  transactions  ? 

5.  A  merchant  sold  a  quantity  of  goods  to  a  customer  at  a 
gain  of  25%,  but  owing  to  the  failure  of  the  customer  he  re- 
ceived in  settlement  but  88^  on  the  dollar.      If  the  merchant 
gained  1645.15,  what  did  the  goods  cost  him  ? 

6.  A  manufacturer  sold  an  article  to  a  jobber  at  a  gain  of 
25%,  the  jobber  sold  it  to  a  wholesaler  at  a  gain  of  20%,  and 
the  wholesaler  sold  it  to  a  retailer  at  a  gain  of  33^%.     If  the 
retailer  paid  1 28  for  the  article,  what  was  the  cost  to  manufac- 
ture it  ? 

7.  A  manufacturer  sold  an  article  to  a  wholesaler  at  a  gain 
of  20%,  the  wholesaler  sold  the  same  article  to  a  retailer  at  a 
gain  of  33  J%,  and  the  retailer  to  the  consumer  at  a  gain  of 
25%.     If   the   average   gain  was  $40,  what  was    the    cost  to 
manufacture  the  article  ? 

WRITTEN   REVIEW  EXERCISE 

1.  A  merchant  bought  goods  at  40  %  off  from  the  list  price 
and  sold  the  same  at  20  %  and  10  %  off  the  list  price.     What 
was  his  gain  per  cent  ? 

2.  I  bought  goods  at  50%  off  from  the  list  price  and  sold 
them  at  25  %  and  25  %  off  from  the  list  price.     Did  I  gain  or 
lose,  and  what  per  cent  ? 

3.  Apr.  15  you  bought  of  Baker,  Taylor  &  Co.,  Rochester, 
N.  Y.,  4000  bbl.  Roller  Process  flour  listed  at  $4.50  a  barrel, 
and   2000  bbl.  of  Searchlight   pastry    flour  listed   at   $4.75  a 
barrel.     Each  list  price  was  subject  to  trade  discounts  of  20  % 
and  10%.    You  paid  cash  $16,000  and  gave  your  note  at  30  da. 
for  the  balance.      What  was  the  amount  of  the  note  ? 

4.  May  18  you  sold  to  F.  H.  Clark  &  Co.,  New  York  City, 
2000  bbl.  of  the  Roller  Process  flour,  bought  in  problem  3,  at 
33J%    above  cost.     Terms:   2/10,  N/3o-     F.    H.    Clark    &    Co. 
paid  cash.     Find  the  cash  payment. 


GAIN   AND   LOSS  257 

5.  May  30  you  sold  Smith,  Perkins  &  Co.,  Albany,  N.Y., 
the  balance  of  the  flour  bought  in  problem  3,  at  an  advance 
of  33J%    on  the  cost.     Terms:  2/io>  N/30.     The  flour  was  paid 
for  June  8.     Find  the  cash  payment. 

6.  What  is  the  net  gain  on  the  transactions  in  problems  3, 
4,  and  5  ?  the  net  gain  per  cent  ? 

7.  Dec.  15  you  bought  of  E.  B.  Johnson  &  Co.  400  bbl.  of 
apples  at  §2.50  per  barrel.     Terms  :  yio,  N/30.     You  paid  cash. 
Find  the  amount  of  your  payment. 

8.  May  15  you  sold  F.  E.  Redmond  the  apples  bought  in 
problem    7,    at   $4    a  barrel.        Terms:       Y10,  N/30.       At  the 
maturity   of   the   bill    Redmond    refused    payment    and   you 
placed  the  account  in  the  hands  of  a  lawyer  who  succeeded  in 
collecting  75  %  of  the  amount  due.     If  the  lawyer's  fee  for  col- 
lecting was  4  %,  what  was  your  net  gain  or  loss  ? 

9.  A  tailor  made  25  doz.  overcoats  with  cloth  worth  $2  a 
yard.      4  yd.   were   required   for    each   coat   and   the   cost   of 
making  was  $48  per  dozen.     He  sold  the  overcoats  so  as  to 
gain  33^%.      How  much  did  he  receive  for  each? 

10.  Apr.  12  J.  D.  Farley  &  Son,  Trenton,  N.  J.,  bought  of 
Cobb,  Bates   &  Co.,   Boston,  Mass.,  a  quantity  of  green  Java 
coffee  sufficient  to  yield  2400  Ib.  when  roasted.     If  the  loss  of 
weight  in  roasting  averages  4%,  what  will  the  green  coffee  cost 
at  30^  a  pound,  less  a  trade  discount  of  10%?     Arrange  the 
problem  in  bill  form. 

11.  If  the  coffee  in  problem  10  is  retailed  33 \%  above  cost, 
and  there  is  a  loss  of  1  %  from  bad  debts,  what  is  the  gain  on 
the  transactions  in  coffee  ?  the  gain  per  cent  ? 

12.  The  Metropolitan  Coal   Co.,  of  Boston,  Mass.,  decides 
to  bid  on  a  contract  for  supplying  2240  T.  of  coal  for  the  pub- 
lic schools  of  the  city.     It  can  buy  the  coal  at  $4.50  per  long 
ton  delivered  on  board  track,  Boston.     It  costs  on  an  average 
75^  per  short  ton  to  deliver  the  coal,  and  there  is  a  waste  of  \  % 
from  handling.     Name  a  bid  covering  a  profit  of  20%.    Terms: 
cash. 


258  PRACTICAL   BUSINESS   ARITHMETIC 

13.    Copy  the  following,  supplying  all  missing  terms 


, 

^.*~7r7;:3^ 


(3?/H-564^^<£^^^?^^ 


\T006  #0 


14.    May  1  you  began  business  investing  18000  in  cash. 
mo.  later  your  resources  and  liabilities  were  as  follows : 


RESOURCES 

Cash  on  hand,  $2500 

Merchandise  on  hand,  1600 

Real  Estate  per  warranty  deed,  5000 
Office  Fixtures  on  hand  597 

Accounts  Receivable  unpaid        1950 


LIABILITIES 

Accounts  Payable  outstanding  $1387 
Notes  Payable  outstanding          3000 


Make  a  statement  showing  your  net  gain  or  loss  and  your 
present  worth  Nov.  1.  Find  the  per  cent  of  gain  or  loss  in 
problem  13 ;  in  problem  14. 


GAIN   AND  LOSS  259 

15.    Copy  the  following  bill,  supplying  all  missing  terms  : 


to. 


flDanufacturing  Co.,  s>r. 


*/. 


y^^^ts^A^frgr^^s/^  sst- 


3/2- a 


/-7V 


16.  If  the  sideboards  in  problem  15  retailed  at  $195  and  the 
parlor    tables    at   $21.25   and   the    delivery    charges   on  sales 
amounted  to  $45.47,  what  was  the  per  cent  of  gain  or  loss  ? 

17.  Copy  the  following  bill,  supplying  all  missing  terms: 


-  Louis,  Mo.,. 


TO  F.  M.  EVERETT  &  Co.,  Dr. 


Terms 


18.    How  much  must  #16  pocket  knives  (problem  17)  retail 
for  apiece  in  order  to  gain  33|%  ?     #20  pocket  knives? 


CHAPTER   XX 

MARKING  GOODS 

319.  Merchants  frequently  use  some  private  mark  to  denote 
the  cost  and  the  selling  price  of  goods.     The  word,  phrase,  or 
series  of  arbitrary  characters  employed  for   private   marks   is 
called  a  key. 

Many  houses  use  two  different  keys  in  marking  goods,  one  to  represent 
the  cost  and  the  other  the  selling  price.  In  this  way  the  cost  of  an  article 
may  not  be  known  to  the  salesmen,  and  the  selling  price  may  not  be  known 
to  any  except  those  in  some  way  connected  with  the  business.  In  large 
houses,  when  but  one  key  is  used,  only  the  selling  price  is  indicated  on  the 
article,  it  being  deemed  best  to  keep  the  actual  cost  of  the  article  a  secret 
with  the  buyers.  In  small  houses,  when  but  one  key  is  used,  both  the  cost 
and  the  selling  price  are  frequently  written  on  the  article. 

320.  If  letters  are  used  to  mark  goods,  any  word  or  phrase 
containing  ten  different  letters  may  be  selected  for  a  key.     If 
arbitrary  characters  are  used,  any  ten  different  characters  may 
be  selected  for  a  key. 

Some  methods  of  marking  are  so  complicated  that  it  is  necessary  to 
always  have  a  key  of  the  system  at  hand  for  reference.  Goods  are  so  marked 
in  order  that  important  facts,  such  as  the  cost  of  goods,  may  be  kept  strictly 
private. 

321.  When  a  figure  is  repeated  one  or  more  times,  one  or 
two  extra  letters  called  repeaters  are  used  to  make   the  key 
word  more  secure  as  a  private  mark. 

The  following  illustrates  the  method  of  marking  goods  by 
letters : 

COST  KEY  SELLING-PRICE  KEY 

REPUBLICAN  PKRTHAMBOY 

1234507890  1234567890 

Repeaters  :  S  and  Z  Repeaters  :  W  and  D 

260 


MARKING   GOODS  261 

The  cost  is  generally  written  above  and  the  selling  price  below  a  hori- 
zontal line  on  a  tag,  or  on  a  paster  or  box.  Gloves  No.  271, 
costing  $5  a  dozen  and  selling  for  $6.25  a  dozen,  might  be 
marked  as  shown  in  the  margin.  Fractions  may  be  desig- 
nated by  additional  letters  or  characters.  Thus,  W  may  be 
made  to  represent  |,  K  |,  etc.  in  the  above  key.  In  marking 
goods  for  the  retail  trade,  all  fractions  of  a  cent  are  called  another  whole  cent. 

WRITTEN    EXERCISE 

Using  the  keys  given  in  §  821,  write  the  cost  and  the  selling 
price  in  each  of  the  following  problems : 

FIRST  COST  FIRST  COST 

OF  OF 

ARTICLE  FREIGHT    GAIN        Loss  ARTICLE      FREIGHT      GAIN        Loss 

1.  $2.50     10%     20%  5.    116.00       2J%     37-|% 

2.  11.00     10%     20%  6.    140.00       5%       16|% 

3.  .50  831%  7.    $  3.60       2-|% 

4.  $4.80     20%  25%     8.    124.00  10% 

Using  the  following  key,  write  the  cost  and  the  selling  price  in 
each  of  the  following  problems  : 

COST  KEY  SELLING-PRICE  KEY 

rL~iJ»--ic:Dj--h      Tj-unEamwi* 

1234567890  1234567890 

Repeaters:     Q        JX^  Repeaters:     X 

FIRST  COST  FIRST  COST 

OF  OF 

ARTICLE    CHARGES    GAIN  Loss  ARTICLE    CHARGES    GAIN    Loss 

9.    $10.00       5%     20%  12.    $15.00      6|%      25% 

10.  $20.00     10%     50%  is.    $18.00      10%      25% 

11.  $30.00     6|%  25%         14.    $12.00        5%    331% 

322.  Wholesalers  and  jobbers  buy  and  sell  a  great  many 
articles  by  the  dozen.  Retailers  buy  a  great  many  articles  by 
the  dozen,  but  generally  sell  them  by  the  piece.  In  marking 
goods,  therefore,  it  is  highly  important  that  the  student  be  able 
to  divide  by  12  with  great  rapidity. 

To  divide  by  12  with  rapidity,  the  decimal  equivalents  of  the  12ths,  from 

to  i    inclusive,  should  be  memorized. 


262 


PRACTICAL   BUSINESS   ARITHMETIC 


TABLE    OF   TWELFTHS 


TWELFTHS 

SIMPLEST 
FORM 

DECIMAL 
VALUE 

TWELFTHS 

1?  I  M  i>  LEST 
FOKM 

DECIMAL 

VALTK 

A 

$.081 

A 

$.581 

a 

* 

.16f 

& 

1 

.6(5| 

A 

i 

.25 

A 

f 

.75 

A 

i 

.88J 

H 

1 

.88$ 

A 

•41| 

H 

.01| 

A 

i 

.50 

if 

1 

1.00 

323.  Example.  What  is  the  cost  of  one  shirt  when  a  dozen 
shirts  cost  $19? 

SOLUTION.  Divide  by  12  the  same  as  by  any  number  of  one  digit  and  men- 
tally reduce  the  twelfths  in  the  remainder  to  their  decimal  equivalent.  Thus, 
say  or  think  1T72,  $1.58$,  practically  $1.58. 

ORAL   EXERCISE 

State  the  cost  per  article  'when  the  cost  per  dozen  articles  is  : 


1. 

$25 

.00. 

7. 

17.00. 

13. 

$23. 

20. 

19. 

$9.00. 

2. 

137 

.00. 

8. 

13.60. 

14. 

$19. 

20. 

20. 

$7.00. 

3. 

$42 

.00. 

9. 

12.40. 

15. 

$66. 

60. 

21. 

$5.00. 

4. 

§64 

.00. 

10. 

$5.60. 

16. 

$38. 

00. 

22. 

$7.50. 

5. 

180 

.00. 

11. 

13.40. 

17. 

$17. 

00. 

23. 

$8.40. 

6. 

$13 

.00. 

12. 

$13.20. 

18. 

$11. 

00. 

24. 

$17.50. 

ORAL  EXERCISE 

1.  Hats  costing  $48  a  dozen  must  be  sold  for  what  price 
each  to  gain  25  %  ? 

2.  Rulers  bought  at  $2  a  dozen   must   be   retailed   at   how 
much  each  to  gain  50  % f- 

3.  Note   books   costing  $1.60   per   dozen  must   be    retailed 
at  what  price  each  to  gain  12|%  ? 

4.  Erasers  bought  at  $3.24  per  gross  must  be  retailed  at 
how  much  each  to  gain  111J%  ? 

5.  Matches  costing  $3.60  per  gross  boxes  must  be  retailed 
at  what  price  per  box  to  gain  100%  ? 


MARKING  GOODS  263 

6.  Envelopes  bought  at  $2  per  M   must  be    sold  at  what 
price  per  package  of  25  to  gain  100%? 

7.  Pickles  bought  at  $  1.80  per  dozen  bottles  must  be  sold 
at  what  price  per  bottle  to  gain  33J  %  ? 

8.  Mustard  costing  114.40  per  gross  packages  must  be  re- 
tailed at  what  price  per  package  to  gain  20%?  to  gain  50%? 

LISTING  GOODS  TOR   CATALOGUES 

324.  In  listing  goods  for  catalogues  dealers  generally  mark 
them  so  that  they  may  allow  a  discount  on  the  goods  and  still 
realize  a  profit. 

325.  Example.    What  should   be  the  catalogue  price  of   an 
article  costing  $24  in  order  to  insure  a  gain  of  25%  and  allow 
the  purchaser  a  discount  of  20  %  ? 

SOLUTION.     \  of  $24  =  §6,  the  gain. 

$30  =  the  selling  price,  which  is  20%  below  the  catalogue  price. 

.80  of  the  catalogue  price  =  $80. 

.-.  the  catalogue  price  =  $30  -=-  .80  =  $37-50 

WRITTEN  EXERCISE 

1.  At  what  price  must  you  mark  an  article  costing  $400  to 
gain  25  %  and  provide  for  a  20  %  loss  through  bad  debts  ? 

2.  What  should  be  the  catalogue  price  of  a  library  table 
costing  $25  in  order  to  insure  a  gain  of  20%  and  allow  the 
purchaser  a  discount  of  25  %  ? 

3.  You  list  tea  costing  30  $  a  pound  in  such  a  way  that  you 
gain  331%  after  allowing  the  purchaser  a  trade  discount  of 
20  %.     What  is  your  list  price? 

4.  You  buy  broadcloth  at  $3.80  per  yard.  .  At  what  price 
must  you  mark  it   in    order   that  you  may  allow  your   cash 
customers  5  %  discount  and  still  realize  a  gain  of  20  %  ? 

5.  Having   bought  a  quantity  of   oranges  for  $3.00  per  C 
you  mark  them  so  as  to  gain  33^%  and  allow  for  a  20  %  loss 
through    bad    debts.     What   will   be   your   asking   price   per 
dozen? 


264 


PRACTICAL   BUSINESS   ARITHMETIC 


6.    At  what  price  must  the  articles  in  the  following  invoice 
be  listed  to  gain  20  %  and  allow  discounts  of  25  %  and  20  %  ? 

Boston,  Mass.,          Nov.     24,    19 

Mr.  Edgar  C.  Towns  end 

Rochester,  N.Y. 

Bought  of  WELLS,  FOWLER  &  CO. 

Terms  Net   30  da. 


#721 
#924 

50 
25 

Oak  Bookcases           $8.00 
Gentlemen1  s  Chiffoniers   12.00 

Less  10$ 

400 
300 

630 

700 
70 

WRITTEN  REVIEW   EXERCISE 

1.  Using  the  word  importance,  with  repeaters  s  and  w,  for 
the  buying  key,  and  the  words  buy  for  cash,  with  repeaters  t 
and  m,  for  the  selling  key,  write  the  cost  and  selling  price  of 
the  articles  in  the  following  bill.  It  is  desired  to  gain  25  %  on 
the  pens  and  pencils,  20%  on  the  cards,  and  to  provide  for  a 
loss  of  12£  %  through  bad  debts. 

Boston,  Mass.,        Oct.    18,    19 

Messrs.   WHITE  &  WYCKOFP 

Holyoke,    Mass. 

Bought  of  C.  E.  Stevens  &  Co. 

Terms  Net  30  da. 


100 

gro.  Pens          $0.80 

80 

25 

"   Lead  Pencils   3.20 

80 

50 

pkg.  Record  Cards     .40 

20 

180 

Less  12  1/2? 

22 

50 

157 

50 

MARKING   GOODS 


265 


2.    At  what  price  must  I  mark  the  following  shoes  to  gain 
20  %  ? 


it,  Mich., 


IQ 


Terms 


*s 


Bought  of  ATWOOD  &  RANDALL 


Jo 


^ 


3.  You  list  tea  bought  for  30^  at  an  advance  of  33^%  on 
the  cost.     Finding  small  sale  for  the  article  you  determine  to 
sell  so  as  to  gain  but  16|%.     What  trade  discount  should  you 
allow  ? 

4.  What  price  per  pound  must  be  obtained  for  the  follow- 
ing invoice  of  coffee  to  gain  25  %  and  allow  10  %  for  loss  in 
roasting  and  16|  %  for  loss  through  bad  debts? 

^o^/o/z,  ^/f«**.,        Nov.    25,    /9 

.   Merchant  &  Co. 

120  Main  St.,    City 

cBougfit  of  Go66,    cBates   &*    So. 

50  days 


2000  Ib.  Green  Java  Coffee  24^ 
Cartage 

480 
2 

00 
50 

482 

50 

CHAPTER   XXI 

COMMISSION  AND  BROKERAGE 
ORAL  EXERCISE 

1.  A  collected   a   bill   of   $350   and  received    6%  for   his 
services.     How  much  did  he  make  ? 

2.  B  bought  |80  worth  of  eggs  for  a  dealer  who  paid  him 
7J-%  for  his  services.     How  much  did  B  make? 

3.  C  receives  $12  a  week,  and  5  %  of  his  weekly  sales.     If 
he  sold  $350  worth  of  goods  in  a  week,  what  was  his  income 
for  the  week  ? 

326.  An  agent  is  a  parson  who  undertakes  to  transact  busi- 
ness for  another  called  the  principal. 

327.  A  great  deal  of  the  produce  of  the  country  and  a  large 
variety  of  manufactured  articles  are  bought  and  sold  through 
agents  called  commission  merchants  and  brokers. 

328.  A  commission  merchant  (sometimes  called  a  factor)  is 
an  agent  who  has  actual  possession  and  control  of  the  goods  of 
his  principal ;  a  broker  is  an  agent  who  arranges  for  purchases 
or  sales  of  goods  without  having  actual  possession  of  them. 

329.  The  sum  charged  by  an  agent  for  transacting  business 
for  his  principal  is  called  commission  or  brokerage. 

Commission  and  brokerage  are  frequently  computed  at  a  certain  per  cent 
of  the  amount  of  property  bought  or  sold,  or  of  the  amount  of  business 
transacted.  Brokerage  is  also  often  a  fixed  rate  per  bushel,  barrel,  tierce, 
or  other  standard  measure. 

330.  Agents    frequently  charge    an    additional    commission, 
called  guaranty,  for   assuming  any  risk   or   guaranteeing  the 
quality  of  goods  bought  or  sold. 

The  person  who  ships  goods  is  sometimes  called  the  consignor;  the  person 
to  whom  the  goods  are  shipped,  the  consignee. 

266 


COMMISSION   AND   BROKERAGE 


267 


A  quantity  of  goods  sent  away  to  be  sold  on  commission  is  called  a  ship- 
ment; a  quantity  of  goods  received  to  be  sold  on  commission,  a  consignment. 

331.  Aii  account  sales  is  an  itemized  statement  rendered  by  a 
commission  merchant  to  his  principal.  It  shows  in  detail  the 
sales  of  the  goods,  the  charges  thereon,  and  the  net  proceeds 
remitted  or  credited. 

^Buffalo,  JV.y.,       June  18.    /9 

Sate  of \*A€.enc/ianciise  for  ^Jccount  of 

E.   H.    Barker  &  Co.,    Poughkeepsie,   N.Y. 

t    iSayto/*  dr* 


| 

June 

5 

200  bbl.  Roller  Process  Flour      $6.00 

1200 

00 

12 

300  "   Old  Grist  Mill  Flour       6.10 

1830 

00 

(2/targes 

June 

2 

Freight  and  Drayage 

40 

75 

12 

Commission  5% 

151 

50 

18 

Net  proceeds  remitted 

2837 

75 

3030 

00 

3030 

00 

332.  An  account  purchase  is  a  detailed  statement  rendered 
lyy  a  purchasing  agent  to  his  principal.  It  shows  in  detail  the 
quantity,  grade,  and  price  of  goods  purchased,  the  expenses 
incurred,  and  the  gross  (total)  cost  of  the  transaction. 


Purchase  of  Merchandise  for  Account  of 


imt  »f  -r^^^rf^^ 


^ 


By  GRAY,  DUNKLE  &  CO. 


t^L    60i 


Charges 


37 


4-7 


268  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  I  sold  100  A.  of  land  at  $50  per  acre  on  a  commission  of 
3%.     What  was  my  commission? 

2.  A  lawyer  collected  an  account  of  $1000  and  received  for 
his  services  $40.      What  was  his  rate  of  commission  ? 

3.  A  book  agent  received  25  %  on  all  books  sold.     In  one 
week,  after  paying  his  expenses,  $25,  lie  netted  $75.     What 
was  the  gross  amount  of  the  week's  sales  ? 

4.  I  bought  through  a  broker  1000  bu.  of  wheat  quoted  at 
89|y  per  bushel.     If  the  broker  charged  -J^  per  bushel  for  buy- 
ing the  wheat,  what  was  his  brokerage  ?     How  much  did  the 
wheat  cost  me  ? 

SELLING   ON   COMMISSION 

WRITTEN   EXERCISE 

1.    Copy  and  complete  the  following  letter  : 
JOHNSON  &  CO. 

Produce  Merchants  ^^^ 

Boston,  Mass.,_       S//>z?^ts  / 0  .        TQ 


vSTUDENT'S    NAME) 


(STUDENT'S  ADDRESS) 


^t^L^i^^^^^ 

J  f&^t^t^J 
~^^L^^^L^-^ 

i^^^z^^'t^^^ 


COMMISSION   AND   BROKERAGE 


269 


2.  May  15  you  sell  F.  E.  Spencer,  Brattleboro,  from  John- 
son &  Co.'s  consignment  :  200  tubs,  10,000  lb.,  creamery  butter 
at  23^,  and  100  crates,  3000  doz.,  eggs  at  20^,  f.o.b.  cars  Brat- 
tleboro.    You  pay  freight  1  16  and  drayage  82.50.     The  terms 
are  2/10,  N/30.     F.  E.  Spencer  pays  cash.     Make  a  receipted  bill 
for  the  transaction. 

3.  May  23  you  sell  Comstock  &  Co.,  Montpelier,  from  John- 
son &  Co.'s  consignment  :  100  crates,  3000  doz.,  eggs  at  20  ^,  and 
100  boxes,  6000  lb.,  cheese  at  12^,  f.o.b.  Montpelier.    You  pay 
freight  $25  and  drayage  $4.50.     Terms:  2/io'  Vso-     Comstock 
&  Co.  pay  cash.     Make  a  receipted  bill  for  the  transaction. 

4.  Render  Johnson  &   Co.   an  account  sales  for  the  goods 
shipped  May  10.     (See  form,  page  267.)     The  net  proceeds 
are  remitted  by  New  York  draft.     Commission,  5%. 

5.  Find  for  Johnson  &  Co.,  the  net  gain  on  the  shipment 
in  problem  1.     The  eggs  were  bought  at  12^,  the  creamery 
butter  at  15^,  and  the  cheese  .at  8^.     Johnson  &  Co.  prepaid 
freight  on  shipment  to  you,  $38.50. 

6.  Pay  freight  $20.50  on  the  merchandise  enumerated  in  the 
following  shipping  invoice.     This  sum  is  5  %  of  the  cost  of  the 
goods.     Find  the  gross  cost  of  the  goods. 


New 


Invoice  of  Merchandise  shipped  to 

J 


(STUDENTS  NAME) 


(STUDENT'S  ADDRESS) 


To  be  sold  for  account  of  C.  L.  BROtTN  &  CO. 


7.  Dec.  15  you  sell  Morgan  &  Co.,  Albany,  N.Y.,  60  bx. 
lemons  at  $4.  Terms:  2/i<r  N/so-  Morgan  &  Co.  pay  cash. 
What  is  the  amount  of  the  cash  payment  ? 


270  PRACTICAL   BUSINESS   ARITHMETIC 

8.  Dec.  18  you  sell  Meachum  &  Co.,  Troy,  N.Y.,  50  bx. 
oranges  at  $4.50.     Terms:  2/io'  N/30.     Meachum  &  Co.  pay  for 
the  goods  Jan.  12.     What  rs  the  amount  of  their  payment? 

9.  Render  C.  L.  Brown  &  Co.  an  account  sales  for  the  goods 
received  Dec.  8,  commission,  5  <jo.     Assume  that  .on  Dec.  5  you 
advanced  them  $50  on  the  consignment.      Find  C.  L.  Brown 
&  Co's  net  gain  or  loss  on  the  shipment  in  problem  6. 

10.  Prepare  an  account  sales,  under  the  current  date,  for  the 
following,  sold  by  you,  for  the  account  of  Lewis,  Grayson  &  Co., 
Rochester,  N.Y.":  60  bbl.  Pillsbury's  flour  at  $6.25;  75  bbl. 
XXXX  flour  at  $5.7£;  45  bbl.  star  brand  flour  at  $5  ;  100  bbl. 
XXX  flour  at  $4.90  ;  50  bbl.  peerless  flour  at  $5.15.  Charges  : 
freight,  $38.95;  cartage,  $12.60;  cooperage,  $6.25;  commis- 
sion, 3|  %  ;  guaranty,  \%. 

BUYING   ON   COMMISSION 

WRITTEN  EXERCISE 

1.  B,  a  broker,  bought  for  C,  a  speculator,  3000  bu.  wheat 
at  90 jy,  on  a  commission  of   \$  per  bushel.     What  was  the 
broker's  commission,  and  what  did  the  wheat  cost  C? 

2.  I  bought  through  a  broker  5000  bags  coffee,  each  con- 
taining 130  lb.,  at  12|,^.     If  the  broker  charged  $10  for  each 
250  bags,  how  much  did  he  earn  on  .the  transaction,  and  what 
did  the  coffee  cost  me? 

3.  I  bought  through  a  broker  20,000  bu.  of  wheat  at 
and  three  weeks  later  sold  it  through  the  same  broker  at 

If  the  broker  charged  me  -^  per  bu.  for  buying  and  the  same 
for  selling,  what  was  rny  gain  ? 

4.  A  firm  of  produce  dealers  bought  through  a  broker  1500 
bbl.  pork  at  $12.50,  and  immediately  sold  it  through  another 
broker  at  $12.721.     If  each  broker  charged  a  commission  of 
2J^  per  barrel,  what  was  gained  by  the  produce  dealers? 

5.  You  buy  for  your  principal  1500  bbl.  flour  at  $4.50,  on  a 
commission  of  3%,  and  pa}^  drayage  $18.50.     What  is  the  cost 
of  the  purchase  to  your  principal? 


COMMISSION   AND   BROKERAGE 


271 


6.  By  your  principal's  instructions  you  put  the  flour  (prob- 
lem 5)  in  storage  and  later  sold  it  at  15.25  a  barrel,  on  a  com- 
mission  of   8%.     The   storage    charges  were    5^   per   barrel. 
What  amount  should  you  remit  to  your  principal  ? 

7.  A  broker  bought  cotton  for  a  manufacturer  as  follows : 
Y50  bales,  375,000  Ib.  at  10-J* ;  1500  bales,  750,000  Ib.  at  lOf  ^; 
and  1000  bales,  500,000  Ib.  at  lOf  f.    The  broker's  charges  were 
$5  for  each  100  bales.     How  much  did  he  earn  on  the  trans- 
action, and  what  did  the  cotton  cost  the  manufacturers? 

8.  Find  the  amount  to  be  charged  to  Roe  &  Co.: 

NEW  YORK,  'N.Y.,  Mar.  15,  19 
Purchased  by  ARAULT  &  Co. 

For  the  account  and  risk  of  ROE  &  Co. 
TELEPHONE,  690  MAIN  Poughkeepsie,  N.Y. 


20 
20 

hf.  ch.  Japan  Tea                          1200  #        30^ 
hf.  ch.  Oolong  Tea                         1000  #        45^ 
Charges 
Drayage 
Commission,  2%,  $      ;  guaranty,  £%,  $ 
Amount  charged  to  your  account 

4 

50 

9.    Find  the  rate  of  commission  and  the  amount  due  Brown 
Bros.  Co.  in  the  following  account  purchase. 

ROCHESTER,  N.Y.,  Apr.  20,  19 
Purchased  by  BROWN  BROS.  Co. 

For  the  account  and  risk  of  W.  D.  SNOW, 
Telephone,  1291  Main  Springfield,  Mass. 


600  bbl.  Pillsbury's  Best  Flour                       6.00 
100  bbl.  xxxx  Flour                                         5.50 
200  bbl.  Peerless  Flour                                   5.25 
Charges 
Cartage 
Commission  ?  % 
Amount  due  us 

15 
104 

00 
00 

272  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN   REVIEW  EXERCISE 

1.  An   agent   bought    for  me  a  consignment  of  flour.     He 
charged  3%  and  received  as  his  commission  §38.40.     I  sold 
the  flour  at  a  gain  of  20  %.     What  was  my  gain  ? 

2.  A  commission  merchant  sold  5000  bu.  grain  and  charged 
\\t  per  bushel  for  selling.     If  the  grain  was  sold  at  49^  per 
bushel,  what  sum  did  he  remit  to  his  principal  ? 

3.  I  paid  a  grain  merchant  122.26  for  selling  a  quantity  of 
grain.     If  he  charged  2  %  commission  and  sold  the  grain  at 
$1.06  per  bushel,  how  many  bushels  did  he  sell  ? 

4.  The  net  proceeds  of  a  consignment  were  §593.75.     The 
following  were  the  different  charges:  commission,  $26;  freight, 
$8.55;    drayage,  $3.40;    storage,  $9.20;    advertising,  $3;    in- 
surance, $6.10.     What  was  the  rate  of  commission  ? 

5.  During    the    months    of    July    and    August    a    college 
student  traveled  for  the  Lester  Manufacturing  Co.,  receiving 
a  commission  of  10  %  on  all  sales.     After  paying  his  expenses, 
$140.60,  he  had  left  as  his  net  earnings  $159.40.     What  was 
the  value  of  the  goods  sold  ? 

6.  A  commission    merchant  charged    3|-%    commission  and 
1J%  guaranty  for  buying  a  stock  of  provisions.     If  the  com- 
mission merchant  received  $22,  what  sum  should  the  principal 
remit  to  cover  cost  of  the  provisions,  commission,  and  guaranty? 

7.  B  was  given  a  difficult  account  for  collection,  with  the 
assurance  that  he  should  receive  25  %  of  all  he  might  collect. 
He  collected  the  account  and  remitted  to  the  holder  $198.42. 
What  was  the  amount  collected  ? 

8.  A  firm  of  contractors  employed  an  agent  to  collect  their 
overdue  accounts.     As  a  special  inducement  for  closing  the 
accounts,  they  were  to  give  him  6  %  on  all  collections  made  the 
first  month,  and  3^  %  on  all  collections  made  the  second  month. 
The  first  month  he  returned  to  the  firm  $4013.80;    the  second 
month  he  returned  $2798.50.     The   returns  were   made   after 
taking  out  his  commission.      What  was  the  agent's  commission  ? 


CHAPTER   XXII 

PROPERTY  INSURANCE 
FIRE  INSURANCE 

ORAL  EXERCISE 

1.  One  hundred  persons  have  property  valued  at  $ 500,000. 
They  pay  into  a  common  fund  |  %  of  this  sum ;   what  is  the 
amount  of  the  fund? 

2.  These  one  hundred  persons  live  in  widely  separated  parts 
of  the  country.     Is  it  likely  that  many  of  them  will  suffer 
losses  by  lire  in  the  same  year  ? 

3.  Suppose  the  losses    to  this  property  by  fire  for  a  year 
amount  to  $  2500.     What  portion  of  the  common  fund  remains 
on  hand  as  a  surplus?     (No  interest.) 

4.  If  this  surplus  is  divided  among  the  100  persons  at  the 
end  of  the  year,  how  much  should  A,  who  paid  in  $30,  receive? 

5.  What  are  the  companies  organized  to  receive  and  control 
the  fund  in  problem  1  called? 

333.  Insurance  is  a  contract  whereby  for  a  stipulated  con- 
sideration one  person  agrees  to  indemnify  another  for  loss  on  a 
specified  subject  by  specified  perils.      The  main  heads  of  prop- 
erty insurance  are  fire  insurance  and  marine  insurance. 

There  are  also  companies  which  insure  against  steam-boiler  explosions, 
failure  of  crops,  death  of  cattle,  burglary,  interruption  to  business  by  strikes 
among  employees,  and  numerous  other  hazards. 

334.  Fire  insurance  is  insurance  against  loss  of  property  or 
damage  to  it  by  fire. 

Fire  insurance  contracts  frequently  cover  loss  caused  by  lightning,  cy- 
clones, and  tornadoes.  Fire  insurance  companies  are  liable  for  loss  resulting 
from  the  use  of  water  applied  for  the  purpose  of  extinguishing  flames; 
also  for  the  destruction  of  buildings  to  prevent  fire  from  spreading. 

273 


274  PRACTICAL   BUSINESS   ARITHMETIC 

335.  The  insurer,  sometimes  called  the  underwriter,  is  the  one 
who  agrees  to  indemnify.     The  insured  is  the  one  to  whom  the 
promise  of  indemnity  is  made.     The  premium  is  the  considera- 
tion agreed  upon.     The  policy  is  the  written  contract. 

336.  Insurance  companies  are  usually  either  stock  companies 
or  mutual  companies.     A   stock   insurance  company  is   one   in 
which  the  capital  is  subscribed,  paid  for,  and  owned  by  persons 
called  stockholders,  -who  share  all  the  gains  and  are  liable  for 
all  the  losses.     A  mutual    insurance  company  is  one  in  which 
the  policy  holders  share  the  gains  and  bear  the  losses. 

In  a  mutual  insurance  company  there  are  no  stockholders,  and  the  capital 
stock  consists  of  the  reserve  earnings  and  investments  of  the  company. 

337.  Policies  of  insurance  are  of  various  kinds.     It  is  neces- 
sary to  distinguish  between  the  valued  and  the  open  policy.     A 
valued  policy  is  one  that  states  the  amount  to  be  paid  in  case  of 
loss.     An  open  policy  is  one  in  which  the  amount  to  be  paid  in 
case    of    loss,    not    exceeding   a   certain    sum,   is    left    to    be 
determined  by  evidence  after  the  loss  occurs. 

Valued  policies  are  very  generally  used  in  the  insurance  of  ships,  but  not 
in  the  insurance  of  cargoes.  Open  policies  are  generally  used  in  fire 
insurance. 

338.  The  standard  form  of  fire  insurance  policy  states  the 
maximum  amount  for  which  the  company  is  liable,  and  this 
amount  is  used  as  a  basis  for  computing  premiums. 

If  a  loss  either  total  or  partial  occurs  under  such  a  policy,  the  company 
is  bound  to  pay  only  so  much  of  the  sum  stated  in  the  policy  as  will 
indemnify  the  insured;  e.g.  if  a  building  insured  for  $3000  is  damaged  by 
fire  $400,  only  the  actual  loss,  $400,  can  be  recovered;  but  if  the  same 
building  were  damaged  by  fire  $3500,  the  company  could  not  be  held  for 
more  than  the  sum  stated  in  the  policy,  $3000. 

339.  Many    fire    insurance    policies   contain    a   co-insurance 
clause  to  the   effect  that  the   person   insured    shall   keep   his 
property  insured  for  a  certain  per  cent  of  its  value,  and  that  if 
he  fails  to  do  this,  the  company  will  pay  him  only  that  propor- 
tion of  the  loss  which  the  per  cent  insured  bears  to  the  per  cent 
named  in  the  policy. 


PROPERTY   INSURANCE  275 

Thus,  the  value  of  a  piece  of  property  is.  $  10,000,  and  the  insured  agrees  to 
keep  it  insured  for  80%  of  its  value,  or  $8000,  but  fails  to  do  so  and  carries 
only  $6000  insurance.  Should  a  loss  occur,  the  company  will  pay  only 
three  fourths  (f  jHHO  of  the  amount  of  such  loss. 

340.  The  rate  of  premium  is  determined  by  the  character 
of  the  risk  and  the  length  of  time  for  which  the  policy  is  issued. 
It  is  sometimes  stated  as  a  per  cent  of  the  amount  insured  and 
sometimes  as  a  certain  rate  on  $100. 

In  some  localities  insurance  agents  sometimes  charge  a  small  fee  for 
surveying  the  premises  and  making  out  a  policy,  but  the  practice  is  not 
common. 

Insurance  is  usually  effected  for  one  or  more  years.  Short  rates  are 
charges  made  for  a  term  less  than  one  year ;  they  are  proportionately  higher 
than  yearly  rates. 

ORAL  EXERCISE 

1.  What  is  the  cost  of  16500  insurance  at  |  %  ? 

2.  What  is  the  premium  on  a  14000  policy  at  \\  %  ? 

3.  What  is  the  cost  of  $6000  worth  of  insurance  at  75^  per 
$100? 

4.  B  insures  a  16000  barn  for  f  value  at  \%.     What  quar- 
terly premium  should  he  pay  ? 

5.  A  insures  a  16000  house  for  |  value,  at  50^  per  $100. 
What  is  the  semiannual  premium  ? 

6.  Goods  worth   $3000    are   insured   for   f   value.     If   the 
annual  premium  is  $  30,  what  is  the  rate  ? 

7.  I  insure  $2400  worth  of  merchandise  for  -|  of  its  value  at 
per  $100.     What  premium  must  I  pay  ? 

8.  I  insure  a  stock  of  goods  worth  $  8000  for  $6000  at  2  %. 
The  goods  became  damaged  by  fire  to  the  extent   of   $3000. 
Under  a  standard  fire  insurance  policy  how  much  can  I  recover  ? 
What  will  be  my  net  loss,  premium  included? 

9.  A  brick  schoolliouse   is   insured   at   50^   per  $100,    the 
annual  premium  is  $50,  and  the  face  of   the   policy  f  of   the 
value  of  the  building.     What  is  the  value  of  the  building  ? 

10.  A  house  valued  at  $20,000  is  insured  in  one  company  for 
$8000.  and  in  another  for  $7000.     A  fire  occurs  by  which  the 
house  is  damaged  $  6000.    How  much  should  each  company  pay  ? 


276 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL   EXERCISE 


State  the  premium  in  each 

FACE 
OF  POLICY  RATE 

1.  $1600  \\% 

2.  $1000  \\% 
State  the  face  of  the  policy 

PREMIUM  RATE 

5.  $9  2% 

6.  $15  li% 
State  the  rate  of  insurance 

FACE 
OF  POLICY  PREMIUM 

9.   $1700  $25.50 

10.   $1850  $37.00 


of  the  following  problems: 

FACE 
OF  POLICY  RATE 

3.  $3500  $1.10  per  $100 

4.  $5000  $1.20  per  $100 

in  each  of  the  folloiving  problems : 
PREMIUM  RATE 

7.  $13.50  $1.35  per  $100 

8.  $24.00  $1.60  per  $100 
in  each  of  the  following  problems : 


FACE 
OF  POLICY 


11. 
12. 


$3200 
$6500 


PREMIUM 

$130.00 
$40.00 


TABLE  OF  ILLUSTRATIVE  RATES 


RISK 

ANNUAL 
RATK     PEK 
$100 

RISK 

ANNUAL 
RATE    PER 
$100 

Frame   carriage    factory    and 

Frame  store  and    dwelling, 

contents 

$1.75 

and  contents 

$0.40 

Frame  dwelling  and  contents 

.25 

Brick  store  and  dwelling,  and 

Brick  business  block  and  con- 

contents 

.25 

tents 

.50 

Brick  church  and  contents 

.50 

Frame  barn  and  contents 

1.00 

Brick  schoolhouse  and  con- 

Brick dwelling  and  contents 

.17 

tents 

.50 

WRITTEN  EXERCISE 

1.  A  in  the  following  diagram  is  a  frame   carriage  factory 
worth  $7000.     Its  contents  are  worth  $8000.      Both  are  insured 
at  |  value.     What  is  the  amount  of  the  annual  premium  ? 

2.  B   is   worth   $3400;    its   contents,    $1200.    C  is   worth 
$1500;  its  contents,  $1100.     All  of  this  property  is  insured 
for  1  yr.  at  |  valuation.     What  is  the  annual  premium  ?     Two 
annual  premiums  in  advance  will  pay  for  three  years'  insurance. 
At  this  rate  what  will  it  cost  to  insure  the  property  for  3  yr.  ? 


J    L 


PROPERTY   INSURANCE 


Street 


277 
J    L 


3.  D  is  worth  $4800.     The  contents  of  the  store  are  worth 
12400  ;   of  the  dwelling,  $800.     What  will  it  cost  to  insure  all 
of  this  property  at   full   value    for  1    yr.  ?     If   three   annual 
premiums  in  advance  will  pay  for  five  years'  insurance,  what 
will  it  cost  to  insure  the  property  for  5  yr.  ? 

4.  E  is  worth  120,000  ;    its  first-floor  contents,  $  4500  ;    its 
second-  and  third-floor  contents,  $7500.      All  are  insured  for 
1  yr.  at  75%  valuation.     What  is  the  amount  of  the  premium? 
A  fire  occurs,  and  the  building  and  contents  are  damaged  to  the 
extent  of  $4500.     If  the  contract  of   insurance  (policy)  con- 
tained an  80%    co-insurance  clause,  how  much  will  the  com- 
pany have  to  pay  ? 

5.  Suppose  that  E  was  insured  in  Company  A  for  $  18,000  at 
the  rate  in  the  table,  and  its  contents  in  Company  B  for  $  10,000 
at  75^  per  $100;  that  both  policies  contained  an  80%  co-insur- 
ance clause;  and  that  the  building  was  damaged  to  the  extent 
of  $3000  and  the  contents  to  the  extent  of  $  2500.     How  much 
would  each  company  have  to  pay  ?     What  would  be  the  net 
loss  to  the  owner  of   the    building  ?  to  the  owner  of  the  con- 
tents?    (Premiums  included  in  each  case,  but  no  interest.) 

6.  F  is  wortli  $10,000  and  its  contents,  $3500.     The  prop- 
erty is  insured  for  one  year  for  $  8100.     If  the  policy  contains 
an  80%  co-insurance  clause,  what  is  the  net  loss  to  the  insurance 
company,  premium  included,  if  the  property  is  destroyed  by  fire  ? 


278  PRACTICAL   BUSINESS   ARITHMETIC 

7.  A,  the  owner  of  G,  has  paid,  annually  for  5  yr.,  insurance 
on  the  dwelling  and  contents.     The  face  of  the  policy  is  $  6000. 
If  the  rate  for  five  annual  premiums  in  advance  is  the  same  as 
three  separate  annual  premiums,   how   much  would  he   have 
gained  had  he  insured  first  for  5  yr.  ?     (No  interest.) 

8.  H    is   worth   115,000   and   its  contents    17500.     Find 
the    cost   of   insuring    80%    of    its    value    for    5    yr.,    three 
annual  premiums  in  advance  paying  for  five  years'  insurance. 

9.  For  insuring  I  and  J  and  contents  at  f  value,  the  owner 
paid  an  annual  premium  of  $22.50.     What  is  the  value  of  the 
property,  the  value  of  J  being  %  of  the  value  of  I? 

10.  K,  worth  f  15,000,  is  insured  in  three  companies  for  | 
value.     Company    A   takes  J  of   the  risk  at  the  price  in  the 
table  ;  Company  B,  |  of  the  risk  at  50^  per  $  100  ;   Company 
C,  the  remainder   at   f  %.     What    was   the    total   premium? 
The  block  becomes  damaged  by  fire  to  the  amount  of  $  6000. 
How  much  will  each  company  be  obliged  to  pay  ? 

11.  I  insured  my  block  of   buildings   with   the   ^Etna   In- 
surance Co.  for  175,000,  at  75^  per  1100.    The  ^Etna  Insurance 
Co.  later  reinsured  $15,000  with  the  Continental  Insurance  Co. 
at  |%  and  $20,000  with  the  German-American  Insurance  Co. 
at  1%.     The  block  became  damaged  by  fire  $20,000.      What 
was  the  net  loss  of  the  ^Etna  Insurance  Co.?     What  was  the 
net  loss  of  the    Continental  Insurance   Co.?  of  the  German- 
American  Insurance  Co.? 

MARINE  INSURANCE 

341.  Marine    insurance    is   insurance   against   loss   to  ships 
and  cargoes  by  perils  of  navigation. 

342.  In    marine    insurance,    the    policies    usually  contain  a 
clause  to  the    effect    that  if  a  vessel    or    cargo,  or  both,    are 
valued  at  more  than   the    amount    insured,  the   insurers   will 
pay  only  such  part  of  the  loss,  either  partial  or  total,  as  the 
amount  insured  bears  to  the  full   valuation.     This  clause    is 
'called  an  average  clause. 


PROPERTY  INSURANCE  279 

Thus,  should  a  vessel  valued  at  $20,000,  and  insured  for  $15,000,  become 
damaged  by  fire  to  the  extent  of  $8000,  under  an  average  clause  policy  the 
company  will  pay  three  fourths  ($$$$%)  of  the  loss,  or  $6000.  Should  the 
same  vessel  and  cargo  be  wholly  destroyed,  the  company  will  pay  the  full 
$15,000,  which  is  three  fourths  of  the  entire  valuation.  In  order  to  be  fully 
protected  in  a  marine  risk,  the  insured  must  insure  his  property  for  full 
value.  Some  fire  insurance  policies  contain  a  clause  similar  to  the  average 
clause  of  marine  insurance  policies.  ^ 

WRITTEN  EXERCISE 

1.  A  vessel  valued  at  $50,000  is  insured   (average   clause 
policy)  for  $18,000  in  Company  A,  and  for  $17,000  in  Company 
B.     A  fire  occurs  by  which  the   vessel  is  damaged  $15,000. 
What  is  the  amount  to  be  paid  by  each  company  ? 

2.  I  paid  $25.40  for  insuring  a  shipment  of  goods  by  steamer 
from  Boston  to  Manila.     If  the  rate  was  1|  %,  less  20%,  what 
was   the   face  of  the  policy  ?     If  the  face  of   the   policy   was 
equal  to  the  value  of  the  goods,  what  would  it  cost  to  make  the 
shipment  by  sailing  vessel  at  1J  %,  less  20%? 

3.  You  take  out  a  $7500  average  clause  policy  on  your  stock 
of  merchandise  worth  $9000.     The  premium  is  75^  per  $100, 
which  you  pay  in  advance.     A   fire  occurs  by  which  the  stock 
is  damaged  $3000.     Estimate  your  total  loss  and  the  net  loss 
to  the  company.      (Premium  included  in  each  case.) 

4.  A  of  Boston  instructed  B  of  Sidney,  Australia,  to  purchase 
$25,000  worth  of  hides.     B  made  the  investment  as  instructed 
and  charged   1J%  commission.     The  hides  were  then  shipped 
by  steamer  and  insured  at  1|  %  for  enough  to  coyer  the  value  of 
the  hides  and  all  charges.     What  was  the  amount  of  the  policy 
and  what  was  the  premium  ? 

5.  A  of  New  York  ordered  B  of  Duluth  to  buy  on  commission 
6000  bu.  of  wheat  and  6000  bu.  of  corn.     B  bought  the  wheat 
at  92^  and  the  corn  at  57^  per  bushel,  and  charged  l|^per 
bushel  commission.      Before  shipping  the  grain  to  A  by  boat, 
B  took  out  a  policy  of  insurance  at  1|  %  to  cover  the  cost  of  the 
goods  and  all  charges.     What  was  the    agent's    commission  ? 
the  insurance  premium  ?     What  did  the  grain  cost  A  ? 


CHAPTER   XXIII 

STATE   AND  LOCAL  TAXES 
ORAL  EXERCISE 

1.  How  are   the   expenses   of   towns,  cities,    counties,   and 
states  met  ? 

2.  A    has   property   worth   $5000    and    B    property    worth 
$  10,000.     How  should  the  taxes  of  these  two  men  compare  ? 

3.  Mention  several  purposes  for  which  taxes  are  raised  in 
your  city  or  town. 

343.  A  tax  is  a  sum  levied  for  the  support  of  government, 
or  for  other  public  purposes.     Taxes  are  of  two  kinds :  direct 
taxes,  which  are  taxes  levied  on  a  person,  his  property,  or  his 
business  ;  indirect  taxes,  which  are  taxes  levied  on   imported 
goods,  and  on  tobacco,  liquors,  etc.,  produced  and  consumed  in 
the  United  States. 

The  expenses  of  town,  county,  city,  and  state  governments  are  met  by 
capitation  or  poll  taxes,  property  taxes,  and  license  fees.  The  expenses  of  the 
National  Government  are  met  chiefly  by  import  duties,  or  customs,  and  excise 
duties. 

344.  A  capitation,  or  poll  tax,  is  a  tax  sometimes  levied  on  each 
male  inhabitant  who  has  attained  his  majority.    A  property  tax  is 
a  tax  levied  on  real  estate  or  on  personal  property.     A  license  fee 
is  a  tax  paid  for  permission  to  engage  in  certain  kinds  of  business. 

Real  estate  and  personal  property  belonging  to  religious  or  charitable 
organizations  are  frequently  exempt  from  taxation. 

345.  Property  taxes  are  imposed  in  nearly  all  the  states  by 
practically  the  same  method,  namely  : 

1.  Officers  called  assessors  are  elected  in  every  city  and 
town,  whose  business  it  is  to  set  a  valuation  upon  all  property 
subject  to  taxation. 

280 


STATE   ANL>   LOCAL   TAXES  281 

2.  In  most  of  the  states  a  County  Board   of  Equalization 
reviews   the   original  assessments,  and  the    judgment   of  this 
body   is   subsequently   passed    upon    by  the    State    Board   of 
Equalization. 

3.  All  the  taxes  for  state  purposes  are  then  equitably  appor- 
tioned among  the  different  counties,  cities,  and  towns.     Each 
county,  city,  town,  and  school  district  also  levies  taxes  for  its 
own  local  expenses. 

Real  estate  is  usually  assessed  at  from  25%  to  33$%  less  than  its  market 
value. 

346.  The  tax  rate  is  expressed  as  so  many  mills  on  the  dollar 
or  so  many  dollars  on  a  hundred  or  a  thousand  dollars. 

The  methods  of  collecting  taxes  vary  somewhat  in  the  different  states. 
A  common  method,  which,  on  the  whole,  seems  satisfactory,  is  for  one  col- 
lector in  each  city  or  town  to  collect  all  the  taxes  —  state,  county,  city  or 
town  —  at  one  time.  If  taxes  are  not  paid,  the  property  taxed  may  be  sold. 
The  purchaser  of  property  sold  for  taxes  is  given  only  a  tax  title  to  it;  but 
this  title  becomes  complete  after  a  certain  period  allowed  the  original 
owner  for  redemption.  In  some  states  if  the  poll  tax  is  not  paid,  the  person 
taxed  may  be  committed  to  jail.  The  compensation  of  a  collector  is  either 
a  fixed  salary  or  a  commission  on  all  taxes  collected. 

ORAL  EXERCISE 

1.  If  the  rate  of  taxation  is  12  mills  on  a  dollar,  how  much 
tax  must  I  pay  on  property  assessed  at  $  5000  ? 

2.  The  tax  rate  is  13  mills  on  a  dollar.      B   has  property 
valued  at  $  8000  and  assessed  at  f  value.     What  is  his  tax  ? 

3.  C  pays  l\%  tax  on  a  city  lot  100  ft.  by  150  ft.,  valued 
at  $1  per  square  foot,  and  assessed  at  f  value.     What  is  the 
amount  of  his  tax  ? 

4.  What  tax  must  I  pay  on  #80,000,  at  5  mills  on  $1,  the 
collector's  commission  being  1  %  ? 

SOLUTION.      .005  of  $ 80,000  =  $400,  the  tax. 

1%  of  the  tax  = 4,  the  collector's  commission. 

$404,  my  property  tax. 

5.  What  tax  must  I  pay  on  $10,000  at  4|  mills  on  $1,  the 
collector's  commission  being  1  %  ? 


282  PRACTICAL   BUSINESS   ARITHMETIC 

6.  If  the  state  tax  is  2  mills,  the  county  tax  3  mills,  and 
the  district  school  tax  |  %,  what  should  you  pay  on  a  farm 
assessed  at  $  3000  ? 

7.  My  total  tax  this  year  was  $61.25.     If  I  have  property 
valued  at  $  10,000,  and  my  poll  tax  amounts  to  11.25,  what  is 
the  rate  of  taxation  ? 

8.  A  collector  turns  over  to  the  county  treasurer  -$8000.     If 
his  commission  was  1|  %  what  amount  did  he  collect?     If  the 
property  taxed  was  worth  $800,000,  what  was  the  rate  of  taxa- 
tion?    Express  this  rate  in  three  ways. 

9.  The  assessed  valuation  of  real  and  personal  property  in 
a  certain  city  is  $400,000,000.     The  city  has  a  bonded  indebt- 
edness of  $  2,000,000,  on  which  it  pays  4  %  interest.     Find  the 
tax  rate  necessary  to  pay  the  interest. 

WRITTEN   EXERCISE 

Find  the  total  tax  : 

1.  Valuation,  $3600;  rate,  $0.016;  3  polls  at  $2. 

2.  Valuation,  $4550;  rate,  9|  mills;   1  poll  at  $1.50. 

3.  Valuation,  $2875;  rate,  $0.0175;  1  poll  at  $1.75. 

4.  Valuation,  $5600;  rate,  $1.12J  per  $100;  1  poll  at  $2. 

5.  Valuation,    $6000;    rate,   $13.40  per  $1000;    2  polls  at 
$1.00. 

Find  the  valuation  : 

6.  Total  tax,  $3800;  rate,  $0,015;  100  polls  at  $2.00. 

7.  Total  tax,  $11,295;     rate  $1.40  per  $100;    250  polls  at 
$1.50. 

8.  Total  tax,  $8850;    rate,  $15.00  per  $1000;    225  polls  at 
$1.00. 

9.  In  a  town  1040  persons  were  subject  to  a  poll  tax;  the 
assessed  valuation  of  real  estate  was  $3,209,400,  and  of  personal 
property  $265,100.     The  polls  were  taxed  $1.25  each.     The  tax 
levy  was  $42,994.     What  was  the  tax  rate  ?    What  was  the  total 
tax  of  Charles  B.  Lester,  who  owned  real  estate  valued  at  $6450, 
and  personal  property  valued  at  $1250,  and  who  paid  for  2  polls  ? 


STATE  AND  LOCAL  TAXES         283 

10.  In  a  town  taxes  were  levied  as  follows  :  state  tax,  $4287  ; 
county  tax,  19312.50  ;  town  tax,  193,156.20.     There  were  1850 
polls  assessed  at  82  each.     If  the  total  property  valuation  was 
$6,245,800,  what  was  the  tax  rate  per  thousand  ? 

11.  A   town  made  provision  by  taxation  for  the  following 
expenses:      public    schools     $18,180;    interest     on    borrowed 
money  $2106;  public  high  ways  $4720;  officials'  salaries  $4620; 
general  expenses  $11,746;  sinking  fund  $8000.     The  value  of 
real  and  personal  property  was  $  2,450,600,  and  2120  polls  were 
assessed   $1.50  each;  $4531.80  was  collected  from  license  fees. 
What  was  the  tax  rate  ? 

12.  A  died  leaving  property  valued  at  $47,950  to  B,  his  son, 
and  property  valued  at  $17,500  to  C,  a  friend.    The  statutes  of 
the  state  in  which  these  three  live  provide  that  B,  a  lineal  heir, 
and  C,  a  collateral  heir,  shall  pay  to  the  state  an  inheritance  tax. 
The  rate  for  lineal  heirs  is  1  %,  and  for  collateral  heirs  5%. 
What  inheritance  tax  must  B  and  C,  respectively,  pay  when 
they  come  into  possession  of  the  property? 

13.  A  city  made  the  following  appropriation  for  its  public 
schools:     teaching  and  supervision,  $36,000;   care  and  cleaning, 
$3360;  fuel,  $3000;  repairs,  $2000;  text-books,  $1700;  supplies, 
$1700;    printing,  $300;   contingent  fund,  $775;  truant  officer, 
$500;  evening  schools,  $1305;   transportation  of  pupils,  $600; 
kindergarten,  $1100;    manual    training,  $700.      The  assessed 
value  of  real  estate  was  $6,709,998   and  of  personal  property 
$2,130,002.     What  was  the  tax  rate  for  school  purposes  ? 

14.  The  market  value  of  a  certain  street  railway  amounts  to 
$20,881,000.     This   amount,   less   the    company's   real   estate, 
machinery,  etc.,  is  subject  to  a  state  corporation  tax  of  $17.25 
per  $1000.     If  the  value  of  the  real  estate,  machinery,  etc.,  is 
$4,570,700,  what  is  the  corporation  tax?     This  corporation  tax 
is  distributed  according  to  trackage  among  the  cities  and  towns 
in  which  the  railway  operates.     If  80%  of  the  trackage  of  the 
road  lies  within  the  city  of  B,  how  much  of  the  state  corporation 
tax  will  that  city  receive? 


284 


PRACTICAL    BUSINESS   ARITHMETIC 


347.  In  order  to  facilitate  clerical  work  a  table  may  be  used 
for  computing  taxes.  The  following  table  was  made  from  the 
published  tax  lists  of  a  city  in  Massachusetts: 

TAX  TABLE.     RATE  $18.60  PER  $1000 


0 

i 

2 

8 

4 

5 

6 

7 

8 

9 

0 

.0000 

.0186 

.0372 

.0558 

.0744 

.0930 

.1116 

.1302 

.1488 

.1674 

1 

.1860 

.2046 

.2232 

.2418 

.2604 

.2790 

.2976 

.3162 

.3348 

.3534 

2 

.3720 

.3906 

.4092 

.4278 

.4464 

.4650 

.4836 

.5022 

.5208 

.5394 

3 

.5580 

.5766 

.5952 

.6138 

.6324 

.6510 

.6696 

.6882 

.7068 

.7254 

4 

.7440 

.7626 

.7812 

.7998 

.8184 

.8370 

.8556 

.8742 

.8928 

.9114 

5 

.9300 

.9486 

.9672 

.9858 

1.0044 

1.0230 

1.0416 

1.0602 

1.0788 

1.0974 

0 

1.1160 

1.1346 

1.1532 

1.1718 

1.1904 

1.2090 

1.2276 

1.2462 

1.2648 

1.2834 

7 

1.3020 

1.3206 

1.331)2 

1.3578 

1.3764 

1.3950 

1.4136 

1.4322 

1.4508 

1.4604 

8 

1.4880 

1.5066 

1.5252 

1.5438 

1.5624 

1.5810 

1.5996 

1.6182 

1.6368 

1.6554 

9 

1.6740 

1.6926 

1.7112 

1.7298 

1.7484 

1.7670 

1.7856 

1.8042 

1.8228 

1.8414 

In  the  table  the  rate  on  each  $1000  was  made  up  as  follows :  state  tax 
$.0807  ;  county  tax,  $.5643  ;  state  highways,  $.003  ;  city  tax,  $17.952.  The 
first  figure  of  the  number  of  dollars  assessed  is  given  at  the  left,  a»d  the 
second  one  at  the  top. 

348.    Example.     What  is  the  tax  on  a  valuation  of  $16,400? 

SOLUTION.     Tax  on  $16,000  =  $297.60  (1000  times  .2976) 
Tax  on          400  7.44  (100  times  .0744) 

Tax  on  $  16,400  =  $  305.04 

WRITTEN   EXERCISE 

Using  the  table,  find  the  tax  on  the  following  valuations: 

1.  12485.  5.      $8,478.         9.    $34,500.         is.    $20,000. 

2.  $1200.  6.    $13,200.        10.    $82,500.         14.    $27,800. 

3.  $1050.  7.    $14,700.        11.    $98,250.         is.    $71,690. 

4.  $4630.  8.    $18,400.        12.    $21,850.         16.    $89,800. 

Find  the  tax  on  the  following  valuations  when  the  collector's 
commission  is  1  %  : 

17.  $5500.          21.   $9500.  25.   $19,000.  29.    $21,000. 

18.  $7500.          22.   $8700.  26.   826,000.  so.   $89,000. 

19.  $2900.          23.   $6500.  27.   $85,000.  si.   $10,000. 

20.  $4700.          24.   $7250.  28.   $78,000.  32.    $21,000. 


CHAPTER   XXIV 

CUSTOMS   DUTIES 
ORAL  EXERCISE 

1.  The  expenses  of  the  National  Government  average  about 
$  1,500,000  per  clay.     What  is  this  per  year  ? 

SUGGESTION.     To  multiply  by  15,  multiply  by  10  and  add  \  of  the  result. 

2.  Name  five  sources  of  income  to  the  National  Government. 

3.  Name  ten  expense  items  of  the  National  Government. 

349.  Duties,  or  customs,  are  taxes  levied  by  the  National  Gov- 
ernment on  imported  goods.     They  are  imposed  in  two  forms : 
ad  valorem  and  specific.     An  ad  valorem  duty  is  a  certain  per 
cent  levied  on  the  net  cost  of  the  importation.      A  specific  duty 
is  a  fixed  sum  levied  on  each  article,  or  on  each  pound,  ton, 
yard,  or  other  standard  measure,  without  regard  to  the  cost. 

Ad  valorem  duties  are  not  computed  on  fractions  of  a  dollar.  If  the 
cents  of  the  net  cost  are  less  than  fifty,  they  are  rejected;  if  fifty  or  more 
than  fifty,  one  dollar  is  added  before  computing  the  duty. 

Some  articles  are  subjected  to  both  ad  valorem  and  specific  duties.  Be- 
fore specific  duties  are  estimated  allowance  is  usually  made  for  tare  and 
breakage.  Specific  duties  are  not  computed  on  fractions  of  a  unit.  Frac- 
tions less  than  £  of  a  unit  are  rejected;  fractions  \  or  more  are  counted  a 
whole  unit.  The  long  ton  of  2240  Ib.  is  used  in  computing  specific  duties. 

350.  A  tariff  is  a  schedule  exhibiting  the  different  rates  of 
duties  imposed  by  Congress  on  imported  articles.     A  free  list  is 
a  schedule  of  imported  articles  exempt  from  duty. 

351.  A  customhouse  is  an  office  established  by  the    National 
Government   for   the   collection  of  duties  and   the   entry  and 
clearance  of  vessels.      A  port  at  which  a  customhouse  is  estab- 
lished is  called  a  port  of  entry;   ports  of  entry  and  other  ports 
are  called  ports  of  delivery. 

286 


286  PRACTICAL   BUSINESS   ARITHMETIC 

The  United  States  is  divided  into  collection  districts,  in  each  of  which 
there  is  a  port  of  entry  and  one  or  more  poi  ts  of  delivery.  All  entries  of 
goods  and  the  payment  of  duties  thereon  must  be  made  at  the  port  of  entry, 
after  which  the  goods  may  be  discharged  at  any  port  of  delivery. 

352.  In  the  most  important  ports   of  the  United  States  the 
customhouse  business  is  distributed  among  three  departments: 

1.  The  collector's  office,  which  takes  charge  of  the  entries  and 
papers,  issues  the  permits,  and  collects  the  duties. 

2.  The  surveyor's  office,  which  takes  charge  of  the  vessel 
and  cargo,  receives  the  permits,  ascertains  the  quantities,  and 
delivers  the  merchandise  to  the  importer. 

3.  The  appraiser's  office,  which  examines  imported  merchan- 
dise and  determines  the  dutiable  value  and  the  rate  of  duty  on 
same. 

One  package  of  every  invoice  and  one  package,  at  least,  out  of  every  ten 
similar  packages  is. sent  to  the  appraiser's  store  for  examination.  Merchan- 
dise in  bulk  and  all  heavy  and  bulky  packages  uniform  in  size  and  quantity 
of  contents  are  generally  examined  on  the  wharf. 

353.  A  manifest  is  a  memorandum,  signed  by  the  master  of  the 
vessel,  showing  the  name  of  the  vessel,  its  cargo,  and  the  names 
and  addresses  of  the  consignors  and  consignees.     An  invoice  is  a 
detailed  statement  showing  the  particulars  of  the  goods  imported. 

All  invoices  must  be  made  out  in  the  weights  and  measures  of  the  coun- 
try in  which  the  goods  are  purchased ;  and  if  the  goods  are 'subject  to  an 
ad  valorem  duty  they  must  be  invoiced  in  the  currency  of  the  country  into 
which  they  are  imported.  Invoices  over  $100  must  be  certified  before 
a  United  States  consul,  who  causes  two  copies  of  the  invoice  to  be  made. 
One  of  these  is  sent  to  the  collector  of  the  port  at  which  the  goods  are  to  be 
entered  and  the.  other  is  kept  on  file  in  the  consul's  office. 

When  the  merchandise  is  loaded  on  board  the  vessel  the  shippers  are 
given  a  bill  of  lading  which  acknowledges  the  receipt  of  the  several  pack- 
ages and  agrees  to  deliver  the  same  at  destination.  The  vessel's  commander 
keeps  a  copy  of  the  bill  of  lading  and  from  the  several  that  have  been  issued 
makes  out  his  manifest  of  cargo.  The  shippers  mail  the  invoice  and  bill  of 
lading  to  the  purchaser,  who  fills  out  an  entry  therefrom  and  presents  it 
and  the  invoice  at  the  customhouse  where  the  duties  imposed  by  law  on  the 
several  classes  of  merchandise  are  collected  and  a  permit  issued  for  the  land- 
ing and  delivery  of  the  merchandise,  subject  to  examination. 


CUSTOMS   DUTIES 


287 


354.  The  values  of  foreign  coins  are  periodically  proclaimed 
by  the  Secretary  of  the  Treasury,  and  these  values  must  be 
taken  in  estimating  duties  unless  a  depreciation  of  the  value  of 
the  foreign  currency  expressed  in  an  invoice  shall  be  shown  by 
the  consular  certificate  thereto  attached.  The  following  esti- 
mate of  the  values  of  foreign  coins  was  recently  proclaimed. 

VALUES  OF  FOREIGN  COINS 


COUNTRY 

STANDARD 

MONETARY  UNIT 

VALUE  IN 
U.  S.  GOLD 

Brazil      ....          .     . 

Gold 

Milreis 

$     546 

Denmark,  Norway,  Sweden   . 
France,  Belgium,  Switzerland 
German  Empire   .... 

Gold 
Gold 
Gold 

Crown 
Franc 
Mark 

.268 
.193 

°38 

Great  Britain 

Gold 

4  866^ 

Japan      ...          .... 

Gold 

YPH 

.498 

Mexico    ... 

Silver 

Dollar 

498 

Netherlands     

Gold 

florin 

402 

Philippine  Islands    .... 
Russia     

Gold 
Gold 

Peso 
Ruble 

.500 
.515 

The  lira  of  Italy,  and  the  peseta  of  Spain,  are  of  the  same  value  as  the 
franc.  The  dollar,  of  the  same  value  as  our  own,  is  the  standard  of  the 
British  possessions  of  North  America,  except  Newfoundland. 

355.  Depositing  goods  in  a  government  or   bonded  ware- 
house is  called  warehousing. 

Many  importers  buy  foreign  goods  in  large  quantities,  withdraw  a  part  of 
them,  and  store  the  remainder  in  the  government  warehouse.  The  goods  so 
deposited  may  be  taken  out  at  any  time  in  quantities  not  less  than  an  entire 
package,  or  in  bulk,  if  not  less  than  one  ton,  by  the  payment  of  duties,  stor- 
age, and  labor  charges.  Foreign  goods  are  sometimes  bought  three  or  four 
months  earlier  than  they  can  be  placed  on  the  market  arid  are  stored  in  the 
government  warehouse  until  they  are  seasonable.  In  this  way  importers 
are  able  to  make  better  selections  and  they  also  get  better  terms  and  prices. 

356.  A  bonded  warehouse   is    a   building    provided    for   the 
storage  of  goods  on  which  duties  have  not  been  paid. 

The  importer  must  give  bond  for  the  payment  of  duties  on  all  goods 
stored  in  a  bonded  warehouse.  Goods  remaining  in  bond  are  charged  10% 


288 


PEACTICAL   BUSINESS   ARITHMETIC 


additional  duty  after  1  yr.  Goods  left  in  the  government  warehouse  beyond 
3  yr.  unclaimed  are  forfeited  to  the  government  and  sold  under  the  direction 
of  the  Secretary  of  the  Treasury.  Goods  may  be  withdrawn  from  a  bonded 
warehouse  for  export  without  the  payment  of  duty. 

357.  The  two  common  forms  of  entry  under  which  duties 
are  collected  are  known  as  inward  foreign  entry  and  warehouse 
entry.     The    former    is    used    for   merchandise    entered    for 
consumption;  the  latter   for  merchandise  that  is  placed  in  a 
bonded  warehouse  under  charge  of  the  government  storekeeper. 

358.  Excise  duties  are  taxes  levied  on  certain  goods  produced 
and  consumed  in  the  United  States.     If  goods,  on  which  either 
excise   or   import   duties    have  been   paid,  are   exported,  the 
amount  so  paid  is  refunded.     The  amount  refunded  is  called  a 
drawback. 


TABLE  OF  DUTIES  ON  CERTAIN  IMPORTS 


DUTY 

ARTICLE  AND  DESCRIPTION 

Specific 

Ad 

Valorem 

Axminster  rugs   . 

10^  per  sq.  yd. 

40% 

Barley,  48  Ib.  to  the  bushel  

30^  per  bu. 

Barley  malt,  34  Ib.  to  the  bushel   
Beans,  60  Ib.  to  the  bushel    .     . 

45^  per  bu. 
45^  per  bu. 

Brussels  carpets 

44  0  Der  so   vd 

40  «/ 

Books          .     .     . 

eu  /o 

25% 

Castile  soap     

l\0  per  Ib. 

Cheese 

60  per  Ib 

China,  porcelain,  and  crockery  ware  
Clocks  and  watches       . 

60% 

40% 

Corn  56  Ib  to  the  bushel 

15  0  per  bu 

Cotton  tablecloths 

50  % 

Hay    . 

$4  per  T. 

"«V     _ 

Ingrain  carpets     
Knit  woolens    

22^  per  sq.  yd. 
44^  per  Ib. 

40% 

50% 

Leather  and  leather  goods     
Marble    

65^  per  cu.  ft. 

20% 
25  "/ 

Plate  glass       .     .     .'  

8  fi  per  sq.  ft. 

Pocket  knives,  value  not  more  than  50^  per  doz. 
Potatoes,  60  Ib.  to  the  bushel     .          ... 

1^  apiece 
25  ft  per  bu. 

40% 

Silk  dress  goods 

11  <j  per  sq    yd 

50  V. 

Sugar      

95  0  r>er  lb. 

Toilet  soap,  all  descriptions  
Wheat     

10IK     r 

15^  per  Ib. 

25  p  per  bu. 

Window  glass  

140  per  Ib. 

CUSTOMS   DUTIES  289 

FINDING   A    SPECIFIC   DUTY 

ORAL  EXERCISE 

Using  the  table  on  page  288,  find  the  duty  on: 

1.  67,200  Ib.  of  hay. 

2.  48,000  Ib.  of  barley. 

3.  100  pc.  plate  glass  24"  x  30". 

4.  2400  Ib.  of  window  glass  10"  x  15". 

5.  A  quantity  of  cheese  weighing  1000  Ib. 

6.  A  shipment  of  wheat  weighing  240,000  Ib. 

7.  A  quantity  of  castile  soap  weighing  2100  Ib. ;  tare  100  Ib. 

WRITTEN  EXERCISE 

1.  Using  the  table  on  page  288,  find  the  total  duty  on: 
2500  bu.  potatoes.     95,000  Ib.  barley.  44,800  Ib.  corn. 
1275  Ib.  toilet  soap.  24,000  Ib.  beans.  10,000  Ib.  cheese. 
6500  Ib.  castile  soap.  136,000  Ib.  barley  malt.  30,000  bu.  potatoes. 

2.  What  is  the  duty  on  175  bx.   castile  soap,  each  weighing 
110  Ib.,  if  5%  is  allowed  for  tare? 

.  3.  Calculate  the  duty  on  10  hogsheads  of  sugar  weighing 
1060-105,  1040-105,  1160-112,  1240-120,  1180-116,  1100-102, 
1090-101, 1100-100,  1005-100,  1210-118  Ib.,  respectively. 

4.  Richard  Roe  &  Co.  imported  from  Canada  3750  bu.  of 
potatoes  invoiced  at  20^  per  bushel.  If  the  transportation 
and  other  charges  amounted  to  1187.50,  how  much  must  be  re- 
ceived per  bushel  for  the  potatoes  in  order  to  gain  25  %  ? 

FINDING   AN   AD   VALOREM   DUTY 

ORAL  EXERCISE 

Find  the  total  duty  : 

1.  On  40  clocks  invoiced  at  $4.50  each. 

2.  On  12  books  invoiced  at  11.50  each. 

3.  On  25  doz.  pocket  knives  invoiced  at  50^  per  doz. 

4.  On  100  sq.  yd.  ingrain  carpet  invoiced  at  81  per  yard 


290  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN  EXERCISE 

Find  the  duty  on  : 

1.  An  Axminster  rug,  12'  x  18',  invoiced  at  £10. 
For  the  values  of  foreign  coins,  see  page  287. 

2.  A  200  lb.  box  of  knit  woolen  goods  invoiced  at  <£100. 

3.  An  importation  of  cotton  table  cloths  invoiced  at  ,£100. 

4.  An  importation  of  cotton  table  cloths  invoiced  at  £  255. 

5.  300  bx.  plate  glass,  each  containing  25  plates  16"  x  24". 

6.  20  Axminster  rugs,  each  12'  x  18',  invoiced  at  £  8  6s. 
per  rug. 

7.  An  importation  of  china  and  crockery  ware  invoiced  at 
100  francs. 

8.  An  invoice  of  knit  woolens  weighing  600  lb.  and  valued 
at  £  315  12*. 

9.  200   blocks   of    marble,    each    10' x  4' x  2',  invoiced   at 
328,000  lira. 

10.  An   importation   of   leather   from    Sweden   invoiced   at 
6750  crowns. 

11.  400  yd.  of  Brussels  carpeting,  |  yd.  wide,  invoiced  at 
82  per  yard. 

12.  4000  meters  of  Brussels  carpeting,  f  yd.  wide,  invoiced 
at  5  francs  per  meter. 

A  meter  equals  approximately  1.1  yd. 

13.  4800  meters  of  silk  dress  goods,  |  yd.  wide,  invoiced  at 
3.75  marks  per  meter. 

14.  A  case  of  silk  dress  goods  containing  200  yd.,  1  yd.  wide, 
invoiced  at  1000  marks. 

15.  An  invoice  of  leather  goods  from  the  Netherlands  in- 
voiced at  12,520  florins. 

16.  5  cs.  of  silk  dress  goods,  each  containing  200  yd.,  |  yd. 
wide,  invoiced  at  20  marks  per  yard. 

17.  I  bought  an  invoice  of  Swiss  watches,  paying  10750  fr. 
for  them  in  Geneva.     What  was  the  total  cost  of  the  watches, 
including  the  duty? 


CUSTOMS   DUTIES 


291 


INVOICES   AND   ENTRIES 

WRITTEN  EXERCISE 

1.    At  what  price  per  pair  must  the  lace  curtains  in  the  fol- 
lowing invoice  be  sold  in  order  to  realize  a  gain  of  33^%  ? 

No.  427  Manchester,  England,         Dec.   15.  zp 

Invoice  of  Lace 
Shipped  by  WILLIAM  P.  FIRTH  6?  CO. 


In  the  Steamer  Catalonia 


To  R.    H.   White  Company 
Boston,    Mass, 


Marks 

No. 

Quantity 

Articles  and  Description 

Price 

Extension 

Amount 

<^ 

317 

50  doz  .  pr  . 

Lace   Curtains 
Less   2% 

Insurance   and  Freight 
Packing  and  Carting 

50%  ad  valorem  duty 

3/2/6 

##*-#*-#* 
*-**-«* 

$***.** 

*#*-**-** 
4-10-6 
16-6 

**#-**-** 
$***  .  ** 
****** 

2.    Find  the  total  cost  of  the  following  invoice: 

Antwerp,  Belgium,        Apr.  2,   19 

Messrs.   A.    T.    Stewart  &  Co. 

New  York  City 

Bought  of  SCHMIDT  &  WESTERFELDT 

Terms  30  da. 


pc.    Black  Silk 

39.00,    40.50.    39.00. 

40.00,  41.00,  40.50 
Insurance  and  freight 
Cartage 

5056  ad  valorem  duty 

11#  per  yd.  specific  duty 


240          Rm.    4 


Rm. 


39.00,  40.50,  etc.,  above,  equal  the  number  of  meters  in  each  piece. 


292 


PRACTICAL   BUSINESS   ARITHMETIC 


3.    Copy  the  following  invoice,  supplying  the  missing  terms 

Bradford,  England,         Dec.  5.   19 
Invoice  of  Woolen  Goods 
Shipped  by    RADCLIFFE    &    SON 

In  the  Steamship  Winifredian         To  R.  H.  Stearns  &  Co. 
Terms  30  da.  Boston,  Mass. 


R 
317 


25 


pc.  Black  Wool  Crepon 
68  69  69  68  69  60  55  60 
56  54  60  60  60  68  68  60 
45  65  65  55  60  65  65  60  60  1544   1/9 

Consul's  fee 


14 


10 


4.  If  the  foregoing  invoice  of  goods  were  entered  for  im- 
mediate consumption,  the  following  is  the  entry  that  would  be 
made  out.  Complete  the  computation  in  the  entry. 


Manifest  No. 


Invoiced  at 


.  /x- 


19— 


INWARD  FOREIGN  ENTRY  OF  MERCHANDISE 

In  the  S^a rn^r7^^^yi^^^L^^/^fy^r^ 


-     ArrivpH 
" 


Mark 


No. 


Packages  and  Contents 


Quantity 


Free  List 


44c.  per  Ib.  + 
60%  ad  valorem 


Duty 


Total 


3/P 


5.  How  much  will  R.  H.  Stearns  &  Co.  have  to  receive  per 
yard  for  the  foregoing  goods  in  order  to  realize  a  gain  of  25%? 

6.  In  a  recent  year  the  receipts  from   customs  duties  were 
1280,000,000,  and  from  excise  duties,  $275,000,000.     The  cus- 
toms duties  for  this  year  were  what  per  cent  greater  than  the 
excise  duties  ?  the  excise  duties  were  what  per  cent  less  than 
the  customs  duties  ? 


CUSTOMS  DUTIES 


293 


7.    Find  the  dutiable  value  and  compute  the  duty  on  the  fol- 
lowing entries  of  merchandise : 


a. 


Manifest  No- 


Invoiced 


\  Q 


INWARD  FOREIGN  ENTRY  OF  MERCHANDISE 


From 


-        In  the  S 

*\^/r-&L4/-4^£- 


the  Steamer 


Arrived. 


Packages  and  Contents  Quantity       ^      valorem       '^C'  PCr  'b'          D"ty          T°Ul 


7* 


*?.?> 


1  kilogram  equals  about  2|^  avoirdupois  pounds.  There  is  no  duty 
charged  on  the  value  of  the  steel  wire,  nor  on  the  quantity  or  value  of  the 
sewing  needles;  but  the  values  of  both  of  these  quantities  is  reduced  to 
United  States  money  by  the  customhouse  officials  for  statistical  purposes. 


Manifest  No. 


Invoiced  at^a* 


INWARD  FOREIGN. ENTRY  OF  MERCHANDISE 

the  Steamer  ~tp£f^L-S. 


A  r ri  ved    (h&^J>7s_.  -3,  \  9 


Mark       No.  Packages  and  Contents 


Quantity       £J 


Free 


60%  ad 
valorem 


65c.  per  Ib.  + 
25%  ad  valorem 


Duty         Total 


J3  ^- 


INTEREST   AND   BANKING 
CHAPTER   XXV 

INTEREST 
ORAL  EXERCISE 

1.  A  borrows  1100  of  B  for  1  yr.     At  the  end  of  the  year 
what  will  A  probably  pay  B  besides  the  face  of  the  loan  ? 

2.  C  puts  $  100  in  a  savings  bank  and  leaves  it  for  1  yr. 
What   can  he    draw  out  at  the  end  of   the  year  besides   the 
money  deposited  ? 

3.  If  you  wished  to  borrow  money  of  a  bank  in  your  town, 
what  rate  of  interest  would  you  have  to  pay  ? 

4.  If  you  loaned  a  man  $>  500  for  1  yr.,  what   would   you 
require  him  to  give  you  as  evidence  of  the  loan  and  security 
for  its  payment  ? 

359.  The  compensation  paid  for  the  use  of  money  is  called 
interest.     Interest  is  computed  at  a  certain  per  cent  of  the  sum 
borrowed.     This  per  cent  of  interest  is  called  the  rate,  and  the 
sum  upon  which  it  is  computed,  the  principal. 

The  rate  of  interest  allowed  by  law  is  called  the  legal  rate.  Persons  rnay 
agree  to  pay  less  than  this  rate,  but  not  more,  unless  a  higher  rate  by  special 
agreement  is  permitted  by  statute.  When  an  obligation  is  interest-bearing 
and  no  rate  is  mentioned,  the  legal  rate  will  be  understood.  An  agreement 
for  interest  greater  than  that  allowed  by  law  is  called  usury. 

360.  In  the  commercial  world,  12  mo.  of  30  da.  each,  or  360 
da.,  are  reckoned  as  1  yr. 

This  method  is  not  exact,  but  it  is  the  most  common  because  the  most 
convenient.  It  has  been  legalized  by  statute  in  some  states  and  is  gener- 
ally used  in  all  the  states. 

294 


INTEREST  295 

SIMPLE   INTEREST 
THE   DAY   METHOD 

ORAL  EXERCISE 

1.  How  many  days  in  a  commercial  year  ? 

2.  What  part  of  a  year  is  60  da.  ?  6  da.  ?  What  is  the  interest 
on  $  1  for  1  yr.  at  6  %  ?  for  60  da.  ?  for  6  da.  ? 

3.  How  do  you  find  .01  of  a  number?  .001  of  a  number? 
What  is  the  interest  on  $120  for  60  da.  at  6  %  ?  for  6  da.  ? 

4.  State  a  short  method  for  finding  the  interest  on  any  prin- 
cipal for  60  da.  at  6  %  ;   for  6  da. 

5.  1  da.  is  what  part  of  6  da.  ?  What  is  J  of  .001  ?  What  is 
the  interest  on  $1200  for  1  da.  at  6  %  ?  on  $180  ?  on  11500  ? 

6.  State    a   short   method  for  finding   the  interest   on  any 
principal  for  1  da.  at  6  %. 

361.  In  the  foregoing  exercise  it  is  clear  that  0.001  of  any 
principal  is  equal  to  the  interest  for  6  da.  at  6% ;  or  0.001  of  any 
principal  is  equal  to  6  times  the  interest  for  1  da.  at  6°/G. 

ORAL  EXERCISE 

1.  Find  the  interest  on  each  of  the  following  for  6  da.  at  6%. 

a.  1250.          e.    $560.        i.    $678.        m.    $290.        q.    $890. 

b.  $870.          /.    $435.       j.    $320.        n.    $150.       r.    $750. 

c.  $358.         g.    $430.        k.    $100.        o.     $325.       s.    $580. 
d:  $350.         h.    $470.        1.    $185.       p.    $990.       t.    $625. 

2.  Find  the  interest  on  each  of  the  above  amounts  for  12 
da.  at  6%  ;   for  18  da.;  for  24  da. 

3.  Find  the  interest  on  each  of  the  following  for  1  da.  at  6  %  • 

a.  $360.          e.    $660.        i.    $600.        m.    $480.       q.    $840. 

b.  $450.         /.    $900.       j.    $180.        n.    $780.       r.    $200. 

c.  $300.         g.    $540.       k.    $720.        o.    $400.       s.    $330. 

d.  $420.         h.    $240.        1.    $500.        p.    $120.       t.    $960. 

4.  Find    the   interest   on   each   of    the    above    amounts   for 
3  da.  at  6%;  for  2  da. 


296  PRACTICAL   BUSINESS   ARITHMETIC 

362.    Example.     Find  the  interest  on  1 450  for  54  da.  at  6  %. 

SOLUTION.    Pointing  off  three  places  to  the  left      54  x  $0.45  =  $24. 30 
gives   $0.45,    or   6  times   the   interest    for    1    da.      &V±  30  —  6  =  84  05 
Multiplying  this   result  by  54  gives   $24.30,    or  6 

times  the  interest  for  54  da.     Dividing  this  result  by  6  gives  $4.05,  the  required 
interest.  9 

By     arranging    the    numbers    as  shown    in    the      54  x  $0.45 
margin  and   canceling    the  work  is  greatly  short-  7»        —  =  $4.05 

ened. 

WRITTEN   EXERCISE 

At  6%  find  the    interest    on    each   of  the  following  problems. 
Reduce  the  time  expressed  in  months  and  days  to  days. 
PRINCIPAL    TIME  PRINCIPAL    TIME  PRINCIPAL  TIME 

1.  $620  54  da.  7.  $900.00  29  da.  13.  $375.80  2  mo.  15  da. 

2.  $175  84  da.  8.  $865.45  93da.  14.  $300.00  3  mo.  19  da. 

3.  $645  42  da.  9.  $700.00  96  da.  15.  $171.15  1  mo.  14  da. 

4.  $300  84  da,  10.  $974.30  62  da.  16.  $120.00  4  mo.  14  da. 

5.  $600  72da.  11.  $178.45  40da.  17.  $211.16  6  mo.  16  da. 

6.  $502  66  da.  12.  $438.55  50  da,  18.  $665.65  1  mo.  10  da. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  $800  for  6  da.  at  3  %  ? 

SOLUTION.     80 ^  is  the  interest  for  6  da.  at  6  %.    3%  is  \  of  6%;  therefore, 
I  of  80^,  or  40  0,  is  the  interest  for  0  da.  at  3%. 

2.  If  the  interest  at  6%  is  $45,  what  is  the  interest  for  the 
same  time  at  3  %  ?  at  12  %  ?  at  2  %  ?  at  1  %  ?  at  1|  %  ? 

3.  Formulate  a  short  method  for  changing  6%   interest  to 
8%  interest. 

SOLUTION.     8%  is  |  more  than  6%;  Hence,  the  interest  at  6%  increased  by 
$  of  itself  equals  the  interest  at  8%. 

4.  State  a  short  method  for   changing    6%  interest  to  7% 
interest;  to  5%  ;  to  9%  ;  to  1\%  ;  to  4|%. 

5.  If  the  interest  at  6%  is  $120,  what  is  the  interest  at  7%? 
a,t  5%  ?  at  8%?     at  4%  ?  at  7-J%?  at  4|-%  ? 


INTEREST  297 

363.  In  the  foregoing  exercise  it  is  clear  that  6%  interest  in- 
creased by  |  of  itself  equals  9  %  interest;  ~by  1  of  itself,  8%  interest; 
by  \  of  itself,  7\  %  interest;  by  1  of  itself,  7  %  interest;  also  that 

6°/o  interest  decreased  by  \  of  itself  equals  4  %  interest ;  by  ^  of 
itself,  4\  %  interest;  by  1  of  itself ,  5%  interest',  also  that 

6  %  interest  divided  by  2  equals  3  %  interest ;  by  3,  2%  inter- 
est; by  6,  1%  interest;  by  4,  1 *  %  interest. 

6  %  interest  multiplied  by  2  equals  12  %  interest. 

6  %  interest  is  changed  to  10  %  interest  by  dividing  by  6  and  removing 
the  decimal  point  one  place  to  the  right;  to  any  other  rate  by  dividing 
by  6  and  multiplying  by  the  given  rate. 

WRITTEN  EXERCISE 

Using  the  exact  number  of  days,  find  the  interest  on : 

1.  12500  from  Sept.  18,  1906,  to  Feb.  6,  1907,  at  9%;  at 
3J%;  at  4%;  at  3%. 

2.  $1700  from  Nov.  20,  1906,  to  Jan.  16,  1907,  at  8%  ;    at 
21  %  ;  at  5|  % ;  at  3J  % ;  at  4  %. 

3.  $2750  from  Dec.  16, 1906,  to  Jan.  17, 1907,  at  7%;  at2%; 
at  4  %  ;  at  5  %  ;  at  1  %  ;  at  10  % . 

4.  $6250  from  Dec.  18,  1906,  to  Feb.  6,  1907,  at  7|  %  ;    at 
10  %  ;  at  11  %  ;  at  4*  %  ;  at  9  %  ;  at  8  % ;  at  7  %  ;  at  3  %. 

THE  BANKER'S  SIXTY-DAY  METHOD 
ORAL  EXERCISE 

1.  60  da.  (2  mo.)  is  what  part  of  a  commercial  year? 

2.  What  is  the  interest  on  $1  for  2  mo.  at  6  %  ?  for  60  da.? 

3.  How  can  you  find  0.01  of  a  number?  What  is  the  interest 
on  $50  for  60  da.  at  6%?  on  $370?  on  $590?  on  $214.55? 

4.  What  fractional  part  of  60  da,  is  30  da.?  20  da.  ?  15  da.  ? 
10  da.  ?     What  is  the  interest  on  $1680  for  60  da.  ?  for  30  da.  ? 
for  20  da.  ?  for  15  da.  ?  for  10  da.  ? 

5.  State  a  simple  way  to  find  the  interest  on  any  principal 
for  60  da.  at  6  %  ;    for  30  da.  ;    for  20  da. ;   for  15  da. ;    for 
10  da. 


298  PRACTICAL   BUSINESS   ARITHMETIC 

6.    Read  aloud  the  following,  supplying  the  missing  words: 
a.  60  da.  minus  ^  of  itself  equals  55  da. ;   60  da.  minus 


of  itself  equals  50  da.  ;   60  da.  minus of  itself  equals  40 

da.  ;   60  da.  minus of  itself  equals  45  da. 

b.    60  da.  plus  -^  of  itself  equals  65  da. ;  60  da.  plus 

of  itself  equals  70  da. ;   60  da.  plus of  itself  equals  75  da. ; 

60  da.  plus  -    -  of  itself  equals  80   da. ;  60  da.  plus of 

itself  equals  90  da. 

7.  What  is  the  interest  on  $600  for  60  da.  at  6%?    for 
55  da.  ?  for  50  da.  ?  for  40  da.  ?  for  45  da.  ? 

8.  What  is  the  interest  on  $1200  for  60  da.?  for  65  da.? 
for  70  da.  ?  for  75  da.  ?  for  80  da.  ?  for  90  da.  ? 

9.  State  a  short  way  to  find  the  interest  at  6%  for  80  da. ; 
for  90  da. ;  for  50  da. ;  for  65  da. ;  for  55  da. ;  for  75  da. ;  for 
70  da. ;  for  40  da. ;  for  45  da. 

364.  In    the   above  exercise  it   is   clear   that  removing   the 
decimal  point  two  places  to  the  left  in  the  principal  gives    the 
interest  for  60  da.  at  6%. 

365.  Examples,    l.    Find  the  interest  on  11950  for  20  da. 
at  6%. 

SOLUTION.  Removing  the  decimal  point  two  places  to  the  left  $19.50 
gives  the  interest  for  60  da.  20  da.  is  \  of  60  da.  \  of  $  19.50  =  a.,,  rn 
$6.50. 

2.    What  is  the  interest  on  $8400.68  for  75  days  ? 

SOLUTION.     Removing  the  decimal  point  two       $$4  0068 
places  to  the  left  gives  the  interest  for  60  da.  ^-i  AA-I  7 

75  da.  is  60  da.  increased  by  £  of  itself  ;  therefore,      

$84.0068  increased  by  \  of  itself  or  §105.01  is  $105.0085,  or  $105.01 
the  required  interest.  In  the  following  exercise  determine  the  separate  interest 
mentally  whenever  it  is  possible  to  do  so. 

WRITTEN  EXERCISE 

1.    Find  the  total  amount  of  interest  at  6%  on: 
$8400  for  60  da.  $8400  for  12  da.  $7900  for  20  da. 

$8400  for  30  da.  $8400  for  10  da.  $7900  for  15  da. 

$8400  for  20  da.  $7900  for  60  da.  $7900  for  12  da. 

$8400  for  15  da.          $7900  for  30  da.          $7900  for  10  da. 


INTEREST  299 

2.  Find  the  total  amount  of  interest  at  6%  on : 

$  1600  for  60  da.  1 1600  for  40  da.          $  2800  for  75  da. 

$  1600  for  55  da.          $  2800  for  60  da.          $  2800  for  80  da. 
$ 1600  for  50  da.  $  2800  for  65  da.          $  2800  for  90  da. 

$ 1600  for  45  da.          1 2800  for  70  da.          $  7200  for  55  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on  : 

$ 1500.60  for  30  da.  $  832.60  for  90  da.  $  8575.65  for  70  da. 
$ 1800.72  for  20  da.  $  720.18  for  10  da.  I  6282.40  for  15  da. 
$ 1200.64  for  15  da.  $ 440.70  for  40  da.  $ 1460.84  for  65  da. 
$ 8400.60  for  10  da.  $ 479.64  for  50  da.  $  1385.62  for  55  da. 

4.  Find  the  total  amount  of  interest  at  6%  on  : 

$  1800.40  for  90  da.  $  7500.00  for  55  da.  $  216.90  for  20  da. 

$  9200.50  for  80  da.  $  8200.00  for  75  da.  $  432.65  for  15  da. 

$  3240.64  for  70  da.  $  6400.00  for  45  da.  $  832.30  for  10  da. 

$4125.18  for  45  da,  11200.45  for  30  da.  $926.17  for  20  da. 

ORAL   EXERCISE 

1.  What  is  the  interest  on  $  215  for  6  da.  at  6  %  ?  on  I  345  ? 
on  1415?   on  1827.50?   on  $425.90?   on  $4520.60?     State  a 
simple   way  to   find  the   interest   on   any  principal  for   6   da. 
at  6%. 

2.  What  part  of  6  da.  is  3  da.  ?  is  2  da.  ?  is  1  da.  ?     What  is 
the  interest  on  $720  for  6  da.?  for  3  da.  ?  for  2  da.  ?  for  1  da.  ? 
State  a  brief  method  of  finding  the  interest  on  any  principal 
for  3  da.  at  6%;  for  2  da.;   for  1  da. 

3.  Read  aloud  the  following,  supplying  the  missing  words : 

a.  6  da.  minus  -J-  of  itself  equals  5  da. ;   6  da.  minus of 

itself  equals  4  da. 

b.  6  da.  plus  ^  of  itself  equals  7  da. ;   6  da.  plus of  itself 

equals  8  da. ;  6  da.  plus of  itself  equals  9  da. 

c.  State  a  short  method  of  finding  the  interest  at  6  %  for  4 
da. ;  for  5  da. ;  for  7  da. ;   for  8  da. ;  for  9  da. 

366.  In  the  above  exercise  it  is  clear  that  removing  the 
decimal  point  in  the  principal  three  places  to  the  left  gives  the 
interest  or  6  da.  at  6. 


300  PRACTICAL   BUSINESS   ARITHMETIC 

367.    Example.    What  is  the  interest  on  $420  for  8  da.  at 

6%? 

SOLUTION.     Removing  the  decimal  point  three  places  to  the  left  gives 
the  interest  for  6  da.,  or  $0.42.     Since  8  da.  is  0  da.  plus  |  of  itself,         »I4U 
$0.42  increased  by  ^  of  itself,  Or  $0.56  is  the  required  interest.     In  the      $.56 
following  exercises   determine  the  separate   interests  mentally  whenever  it  is 
possible  to  do  so. 

WRITTEN   EXERCISE 

1.  Find  the  total  amount  of  interest  at  6  %  on : 

1800  for  6  da.  $720  for  6  da.  $1500  for  6  da. 

$800  for  3  da.  $720  for  7  da.  $1500  for  5  da. 

$800  for  2  da.  $720  for  8  da.  $1500  for  4  da. 

$800  for  1  da.  $720  for  9  da.  $1500  for  9  da. 

2.  Find  the  total  amount  of  interest  at  6%  on  : 

$1168  for  6  da.  $1600  for  6  da.  $2400  for  6  da. 

$1168  for  3  da.  $1600  for  7  da,  $2400  for  5  da. 

$1168  for  2  da.  $1600  for  8  da.  $2400  for  4  da. 

$1168  for  1  da.  $1600  for  9  da.  *2400  for  8  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on  : 

$640.50  for  8  da.  $800.10  for  7  da.  $213.80  for  50  da. 

$920.10  for  20  da.  $240.80  for  90  da.  $310.40  for  40  da. 

$280.40  for  15  da.  $960.70  for  70  da.  $135.90  for  10  da. 

$390.60  for  50  da.  $845.60  for  90  da.  $736.18  for  10  da. 

ORAL    EXERCISE 

1.  600  da.  is  how  many  times  60  da.?     If  the  interest  on  $1 
for  60  da.  at  6  %  is  $0.01,  what  is  the  interest  for  600  da.? 

2.  Give  a  rapid  method  for  finding  0.1  of  a  number.     What 
is  the  interest  on  $500  for  600  da.  at  6  %  ?  on  $350?  on  $214.60? 
on  $359.80?  on  $4500?  on  $9243.80?  on  $750?  on  $2150? 

3.  What    part    of    600  da.  is  300  da,  ?    200  da.  ?   150  da.  ? 
75  da.  ?    120  da.  ?    100  da.  ?    50  da.  ? 

4.  What  is  the  interest  on  $1400  for  600  da.  ?  for  300  da.  ? 
for   200  da.  ?  for  150  da.?  for  75  da.  ?  for  120  da.  ?  for  100 
da.  ?  for  50  da.  ? 


INTEREST  301 

5.  State  a  brief  method  of  finding  the  interest  for  600  da. 
at  6  %  ;   for  300  da.  ;   for  200  da.  ;   for  75  da.  ;   for  50  da.  ;  for 
150  da.  ;  for  200  da. 

6.  If  the  interest  on$l  for  600  da.  is  10.10,  what  is  the  inter- 
est for  6000  da.  ?     In  how  many  days  will  any  principal  double 
itself  at  6  %  interest  ? 

7.  What  is  the  interest  on  $1  for  6000  da.  at  6  %  ?  on  |55  ? 
on  $75.60  ?  on  818.90  ?  on  $350  ?  on  $725  ?  on  $9125.70. 

8.  What  is  the  interest  on  each  of  the  amounts  in  problem 
7  for  3000  da.  ?  for  2000  da.  ?  for  1000  da  ?  for  1500  da..? 

9.  What  is  the  interest  on  $2500  for  6000  da.?  on  $2150? 
on  $7500?  on  $790?  on  $155.60? 

10.    What  is  the  interest  on  each  of  the  amounts  in  problem 
9  for  6  da.  ?  for  60  da.  ?  for  600  da  ? 

368.  In  the  above  exercise  it  is  clear  that  removing  the  deci- 
mal point  in  the  principal  one  place  to  the  left  gives  the  interest 
for  6fJO  da.  at  6%  >  a^so  that  any  sum  of  money  will  double  itself 
in  6000  da. 

WRITTEN   EXERCISE 

Find  the  interest  at  6%  on  : 

1.  $240  for  3000  da.  5.  $7420.50  for  600  da.   9.  $1640  for  150  da. 

2.  $318  for  6000  da.  6.  $67218.90  for  30  da.  10.  $1260.  60  for  1  da. 

3.  $912  for  2000  da.  7.  $8400.50  for  400  da.  11.  $17890  for  10  da. 

4.  $316  for  1500  da.  8.  $7500.79  for  1500  da.  12.  $1696  for  100  da. 

ORAL   EXERCISE 

1.  How  many  times  is  6  da.  contained  in  18  da.  ?  in  24  da.  ? 
in  36  da.  ?  in  42  da.  ?  in  54  da.  ?  in  48  da.  ? 

2.  What  is  the  interest  on  $150  for  6  da.  ?  for  18  da.  ?  for 
48  da.  ?  for  54  da.  ?  for  36  da.  ?  for  42  da.  ?  for  12  da.  ? 

3.  What  is  the  interest  on  $350  for  60  da.  ?  for  180  da.  ? 
for  240  da.  ?  for  360  da.  ?  for  420  da.  ?  for  480  da.  ? 

369.  Example.     Find  the  interest  on  $375  for  48  da.  at  6%. 
SOLUTION.    37£?  equals  the  interest  for  6  da.     48  da.  is  8  times 


6  da.     Therefore,  the  interest  for  48  da.  is  8  times  37$?,  or  $3.  $3.000 


302  PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 

1.  Find  the  total  amount  of  interest  at  6  %  on : 

8750  for  6  da.  $750  for  36  da.  1750  for  60  da. 

1750  for  12  da.  $750  for  42  da.  $750  for  180  da. 

$750  for  18  da.  $750  for  48  da.  $750  for  240  da. 

2.  Find  the  total  amount  of  interest  at  6%  on: 

$725  for  18  da.  $690  for  6  da.  $450  for  540  da. 

$824  for  36  da.  $129  for  60  da.  $727  for  180  da. 

$729  for  42  da.  $475  for  600  da.  $286  for  240  da. 

$850  for  54  da.  $8600  for  54  da.  $429  for  420  da. 

3.  Find  the  total  amount  of  interest  at  6%  on: 
$317.40  for  240  da.    $217.18  for  18  da.      $360.40  for  24  da. 
$218.60  for  180  da.    $420.50  for  24  da.      $860.50  for  48  da. 
$419.80  for  420  da.    $240.70  for  540  da.    $900.60  for  66  da. 
$425.60  for  120  da.    $290.60  for  180  da.    $400.80  for  84  da. 

370.  In  some  cases  it  is  advisable  to  find  the  interest  on  the 
principal  for  1  da.  and  then  multiply  by  the  number  of  days. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  $600  for  17  da.  at  6  %  ? 

SOLUTION.     The  interest  for  one  day  is  .000|  of  the  principal,  or  10^.     The 
interest  for  17  da.  is  17  times  10^,  or  $1.70. 

2.  What  is  the  interest  on  $6000  for  49  da.  at  6/0?  on  $300? 
on  $240?  on  $3000?  on  $1800?  on  $840?  on  $600? 

3.  State  the  interest  at  6jfe  on: 

a.  $600  for  19  da.  e.  $6000  for  37  da.  i.  $  900  for    17  da. 

b.  $300  for  37  da.  /.  $3000  for  43  da.  j.  $1500  for    40  da. 

c.  $240  for  43  da.  g.  $2400  for  67  da.  k.  $   600  for  139  da. 

d.  $180  for  27  da.  h.  $1800  for  89  da.  L  $   300  for  179  da. 

371.  Frequently  it  is  well  to  mentally  divide  the  days  into 
convenient  parts  of  6  or  60. 

Thus,  97  da.  =  60  da.  +  30  da.  +  6  da.  +  1  da. ;  71  da.  =  60  da.  +  10  da, 
+  1  da. ;  49  da.  =  8  times  6  da.  +  1  da. 


INTEREST  303 

ORAL   EXERCISE 

Separate  the  days  in  the  following  exercise  into  6  da.  or  60  da., 
or  into  convenient  parts  of  6  da.  or  60  da. 


1. 

8 

da. 

7. 

7 

da. 

13. 

86 

da. 

19. 

17 

da. 

2, 

67 

da. 

8. 

22 

da. 

14. 

55 

da. 

20. 

25 

da. 

3. 

27 

da. 

9. 

11 

da. 

15. 

84 

da. 

21. 

85 

da. 

4. 

13 

da. 

10. 

63 

da. 

16. 

14 

da. 

22. 

89 

da. 

5. 

72 

da. 

11. 

37 

da. 

17. 

97 

da. 

23. 

19 

da. 

6. 

43 

da. 

12. 

23 

da. 

18. 

99 

da. 

24. 

29 

da. 

372.    Examples.     1.    Find  the  interest  on  1840  for  31  da.  at 
6%. 

SOLUTION.     31  da.  =  30  da.  +  1  da.     The  interest  for  60   da.   is 

$  8.40  and  for  30  da.  1  of  this  sum  or  $  4.20.     The  interest  for  6  da.  is  $4. 20 

$0.84  and  for  1  da.  1  of  this  sum  or  $0.14.     Adding  $4.20  and  $0.14  .14 

the  result  is  the  required  interest,  or  $4.34.  $4  34 

2.    What  is  the  interest  on  $2500  for  121  da.  at  6  %  ? 

125.00 


SOLUTION.     121  da.  =  2  x  60  da.  +  1  da.     The  interest  for  60  da. 
is  $25  and  for  120  da.  twice  this  sum,  or  $50.     The  interest  for  6      §50.00 
da.  is  $2.50  and  for  1  da.  }  of  this  sum,  or  $0.42.     Adding  $50  and  42 

$0.42  the  result  is  $50.42,  the  required  interest. 

WRITTEN  EXERCISE 

Find  the  interest : 


PRINCIPAL          TIME 

RATE 

PRINCIPAL 

TIME         RATE 

1. 

$420 

3 

mo. 

6% 

11. 

$450 

4 

mo.      4|  % 

2. 

$650 

4 

mo. 

5% 

12. 

$600 

2 

mo.      5% 

3. 

$360 

92 

da. 

4% 

13. 

$720 

8 

mo.       3% 

4. 

$250 

30 

da. 

3% 

14. 

$840 

2 

mo.      \\% 

5. 

$380 

24 

da. 

1% 

15. 

$120 

7 

mo.      6% 

6. 

$900 

55 

da. 

6% 

16. 

$280 

9 

mo.      3J% 

7. 

$550 

47 

da. 

3% 

17. 

$885 

.90 

20 

da.       3% 

8. 

$800 

29 

da. 

5% 

18. 

$240 

.00 

21 

da.       6% 

9. 

$400 

90 

da. 

4% 

19. 

$420 

.18 

25 

da.        2-|% 

10. 

$270 

11 

da. 

1% 

20. 

$560 

.17 

27 

da.       6% 

304  PRACTICAL   BUSINESS   ARITHMETIC 

373.  It  has  been  observed  that  6  times  1800  =  800  times  86  ; 
that  0.01  of  1715  =  715  times  $0.01 ;  etc.      Hence, 

374.  The  principal  in  dollars  and  the  time  in  days  may   be 
interchanged  without  affecting  the  amount  of  interest. 

375.  Example.    Find  the  interest  on  $600  for  179 da,  at  6%. 

SOLUTION.  $600  for  179  da.  =  $179  for  600  da.  ;  fa  of  the  principal  equals, 
the  interest  for  600  da.  ;  fa  of  $  179  =  $  17.90,  the  required  interest. 

ORAL  EXERCISE 

State  the  interest  at  6  %  on  : 

1.  860  for  27  da.  11.    I860  for  91  da. 

2.  830  for  13  da.  12.    8420  for  87  da. 

3.  820  for  171  da.  13.    8540  for  21  da. 

4.  810  for  186  da.  14.    8660  for  37  da. 

5.  815  .for  145  da.  15.    8750  for  56  da. 

6.  812  for  179  da.  16.    83600  for  218  da. 

7.  810  for  131  da.  17.    82000  for  183  da. 

8.  8100  for  120  da.  18.    81200  for  155  da. 

9.  8200  for  189  da.  19.    81800  for  181  da. 
10.    8150  for  192  da.                       20.    82400  for  218  da. 

376.  81500  on  interest  for  24  da.  at  8  %  =  82000  (81500  4-  £ 
of  itself)  on  interest  for  24  da.  at  6  %,  or  81500  on  interest  for 
32  da.  (24  da.  +  J  of  itself)  at  6  %.      Hence, 

377.  If  either  the  principal  or  the  time  is  increased  or  decreased 
by  any  fraction  of  itself,  the  interest  is  increased  or  decreased  by 
the  same  fraction. 

378.  Examples.     1.    Find  the  interest  on  8480  for  279  da. 
at  71%. 

SOLUTION.  1\  %  is  \  more  than  6%.  Increase  the  principal  by  \  of  itself,  and 
the  result  is  $600.  Interchanging  dollars  and  days,  the  problem  is  "Find  the 
interest  on  8279  for  600  da."  Pointing  off  one  place  in  the  new  principal,  the 
result  is  §27.90,  the  required  interest. 


2.    Find  the  interest  on  82795.84  for  80  da.  at 


'fo 


SOLUTION.    4£%  is  £  less  than  6%  interest.     80  da.  decreased  by  \  of  itself 
equals  60  da.    The  interest  on  $2795.84  for  60  da.  =  $27.96,  the  required  result. 


INTEREST  305 

ORAL  EXERCISE 

State  the  interest  on  : 

1.  #279.86  for  45  da.  at  4  %.  6.  $2400  for  39  da.  at  5  %. 

2.  $478.65  for  45  da.  at  4  %.  7.  $2700  for  37  da.  at  4  %. 

3.  $  769.64  for  48  da.  at  7J  %.  8.  12400  for  87  da.  at  4J  %. 

4.  $217.49  for  80  da.  at  4|  %.  9.  $  1600  for  95  da.  at  4£  %.. 

5.  1767.53  for  80  da.  at  4J  %.  10.  $3200  for  59  da.  at  4-|  %. 


THE  Six  PER  CENT  METHOD 

379.  This  method  is  best  adapted  to   finding   the   interest 
when  the  time  is  one  year,  or  more  than  one  year. 

ORAL  EXERCISE 

1.  If  the  interest  on  11  for  1  yr.  at  6  %  is  10.06,  what  is  the 
interest  on  $1  for  2  yr.  ?  for  3  yr.  ?  for  4  yr.  ?  for  6  yr.  ?  for 
8  yr.  ?  for  10  yr.  ? 

2.  If  the  interest  on  $1  for  1  yr.  at  6%  is  10.06,  what  is  the 
interest  on  $1  for  1  mo.?  for  2  mo.  ?  for  3  mo.  ?  for  6  mo.? 
for  10  mo.  ?  for  7  mo.  ?  for  8  mo.  ? 

3.  What  is  the  interest  on  $1  for  1  yr.  6  mo.  at  6%?    for 
2  yr.  6  mo.  ?  for  3  yr.  4  mo.  ?  for  3  yr.   6  mo.  ?  for  4  yr.  8 
mo.  ?  for  1  yr.  10  mo.  ?  for  5  yr.  6  mo.  ?  for  2  yr.  9  mo.? 

4.  What  is  the  interest  on  150  for  1  yr.  at  6  %  ?  for  1  yr. 
6  mo.  ?  for  2  yr.  ?  for  3  yr.  6  mo.  ?  for  2  yr.  8  mo.  ?  for  1  yr. 
10  mo.  ?  for  2  yr.  6  mo.  ?  for  4  yr.  6  mo.  ?  for  1  yr.  9  mo.  ? 

5.  If  the  interest  on  §1  for  1  mo.  at  6  %  is  $0.005  (5  mills), 
what  is  the  interest  for  1  da.  ?  for  2  da.  ?  for  3  da.  ?  for  4  da.  ? 
for  6  da.  ?  for  12  da.  ?  for  18  da.  ?  for  28  da.  ?  for  24  da.  ? 

6.  What  is  the  interest  on  $1  for  1  yr.  1  mo.  1  da.  at  6%  ? 
for  2  yr.  3  mo.  3  da.  ?  for  1  yr.  10  mo.  6  da.  ?   for  4  yr.  4  mo. 
24  da.  ?  for  1  yr.  5  mo.  12  da.  ?  for  2  yr.  1  mo.  1  da.  ? 

380.  In  the  above  exercise  it  is  clear  that : 

10.06  =  interest  on  $lfor  I  yr.  at$%. 
$0.005  =  Interest  on  $lfor  1  mo.  at  6  %. 
$0.0001  =  interest  on  $lfor  1  da.  at  6  %. 


306  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL   EXERCISE 

Find  the  interest  on  $1  at  6%  for: 

1.  1  yr.  4  mo.  12  da.                      5.  2  yr.  6  mo.  6  da. 

2.  1  yr.  8  mo.  18  da.                      6.  3  yr.  4  mo.  9  da. 

3.  1  yr.  7  mo.  24  da.                      7.  5  yr.  3  mo.  3  da. 

4.  1  yr.  9  mo.  27  da.                      8.  4  yr.  8  mo.  4  da. 
Find  the  interest  at  6%  on  : 

9.   1250  for  2  yr.  14.   1350  for  3  yr. 

10.  $400  for  5  yr.  15.    1450  for  2  yr.  3  mo. 

11.  1700  for  4  yr.  16.    $150  for  1  yr.  6  mo. 

12.  8300  for  3  yr.  4  mo.  17.    $50  for  1  yr.  2  mo.  6  da. 

13.  $500  for  4  yr.  2  mo.  18.    $10'  for  2  yr.  6  mo.  6  da. 
381.   Example.    What  is  the  interest  on  $600  for  2  yr.  8  mo. 

15  da.  at  6  %  ? 

SOLUTION.    Find  the    $0.12       =  int.  on  $1  for  2  yr. 
interest  on  *1  for  2  yr.;          ^        =   -^  Qn  fl  for  g  mQ> 
on  .$1   for  8  mo.  ;    on 

$1  for  15  da.     The  sum          '^^  =     lnt-  on  *      for  15  da- 
of  these  interest  items    $0.1625  =  int.  on  $1  for  the  given  time. 
equals  $0.1625,  the  in-  (JQO  x  $0.1625  =  $97.50,  int.  on  $600 

terest   on    *]  ^  for    the  f       g          g  15  ^        ^% 

given  time  at  6%.    Mul- 

tiplying this  interest  by  the  given  number  of  dollars,  600,  the  product  is  the 
required  interest,  $97.50.     Change  to  any  other  rate  as  in  §  362. 

Sometimes  it  is  shorter  to  find  the  interest  on  $  1  for  the  given  time  at 
any  given  rate,  and  multiply  by  the  number  of  dollars  in  the  principal. 
Thus  to  find  the  interest  on  $400  for  2  yr.  6  mo.  at  8%,  take  400  times  20  j* 
(2£  x  8^  );  on  $  500  for  5  yr.  3  mo.  at  4  %,  take  500  times  21  ^  (5£  x  8  ^  ; 
on  ^600  for  1  yr.  9  mo.  at  4%  take  600  times  7^;  etc. 


ORAL   EXERCISE 

Find  the  interest  : 


PRINCIPAL 

TIME 

RATE 

PRINCIPAL 

TIME 

1. 

$400 

1 

yr. 

2  mo. 

6% 

7. 

$840 

1 

yr. 

6 

mo. 

2. 

$500 

2 

yr- 

4  mo. 

6% 

8. 

$100 

3 

yr. 

6 

mo. 

3. 

$300 

4 

yr. 

6  mo. 

6% 

9. 

$960 

4 

yr. 

2 

mo. 

4. 

$250 

1 

yr. 

8  mo. 

6% 

10. 

$300 

3 

yr. 

4 

mo. 

5. 

$200 

2 

yr. 

10  mo. 

3% 

11. 

$240 

2 

yr. 

6 

mo. 

6. 

$300 

1 

yr. 

11  mo. 

6% 

12. 

$180 

1 

yr. 

8 

mo. 

RATE 

6% 
5% 
6% 
3% 
4% 
6% 


L 


382.  This  method  employs  a  series  of  tables  in  which  inter- 
est computations  are  already  worked  out,  and  by  the   use  of 
which  the  interest  may  be  found  on  any  sum,  at  given  rates, 
for  any  time. 

This  method  is  used  in  banks,  insurance  offices,  and  kindred  institutions, 
and  it  greatly  lessens  the  work  of  computing  interest.  Many  different  sys- 
tems are  published,  but  the  section  of  an  interest  table  given  on  page  308 
will  illustrate  the  general  plan  followed. 

ORAL  EXERCISE 

1.  What  is  the  interest  (use  the  table,  page  308)  on  1 8  for 
5  da.?  on  $80?  (10  x  18)  ;  on  $800  ?  on  $8000? 

2.  What  is  the  interest  on  $10  for  7  da.?  on  $100?  on 
$1000  ?  on  $10,000?  on  $70  for  5  da.?  on  $700  ?  on  $7000  ? 

3.  What  is  the  interest  on  $4  for  11  mo.  ?   on  $40  for  the 
same  time?  on  $400?  on  $4000?  on  $50,000  for  7  mo.  ? 

383.  Example.    Find  the  interest  on  $9980  for  7  da.  at 

SOLUTION  :    By  the  table,  $  10.50  =  interest  on  $  9000. 
1.05  =  interest  on    $900. 

.09  =  interest  on      $  80. 

$11.64  =  interest  on 


WRITTEN  EXERCISE 

Using  the  table,  find  the  interest  on  : 

1.  $8800  for  4  da.  5.   $17,000  for  1  da. 

2.  $9600  for  5  da.  6.    $29,000  for  1  da. 

3.  $7500  for  7  mo.  7.   $71,000  for  7  da. 

4.  $8500  for  11  mo.  8.    $87,000  for  11  da. 

PROMISSORY  NOTES 

384.    A  written  promise  to  pay  a  certain  sum  of  money  on 
demand,  or  at  a  specified  time,  is  called  a  promissory  note. 


the  order  of 


JDollars 


Value  received 


INTEREST 


309 


Blank  Indorsement 


385.  In  the  foregoing  note  Ellis  B.  Pitkin  is  the  maker; 
William  B.  Harris,  the  payee ;  and  $243.50,  the  face.     The  note 
is  negotiable  ;  that  is,  it  may  be  transferred  by  the  payee  to 
any  other  person  by  indorsement. 

If  the  note  were  drawn  payable  to  William  B.  Harris,  or  bearer,  it  would 
be  transferable  by  delivery  and  would  be  negotiable.  If  the  words  to  the 
order  of  were  omitted,  the  note  would  not  be  transferable  either  by  indorse- 
ment or  by  delivery ;  it  would  be  payable  to  William  B.  Harris  only,  and 
would  be  called  a  non-negotiable  note. 

386.  If  the  payee  should  sell  the  foregoing  note,  he  would 
have  to  indorse  it;  that  is,  make  it  payable  to  the  buyer  by  a 
writing  on  the  back  of  the  instrument.     This  indorsement  may 
be  made  in  either  of  the  three  ways  shown  in. the  margin. 

William  B.  Harris  sold  the  note  to  O.  D.  Merrill  and  effected  the  transfer 
by  a  blank  indorsement.  This  is  simply 
William  B.  Harris's  signature.  It  makes 
the  note  payable  to  bearer.  O.  D.  Merrill 
sold  the  note  to  Andrew  J.  Lloyd  and 
effected  the  transfer  by  a  full  indorsement, 
an  indorsement  which  specifies  the  one  to 
whose  order  the  note  is  made  payable.  By 
indorsing  the  note  both  William  B. 
Harris  and  O.  D.  Merrill  make  themselves 
responsible  for  its  payment  in  case  the 
maker  does  not  pay  it.  O.  H.  Briggs  was 
willing  to  buy  the  note  without  Andrew  J. 
Loyd's  guarantee  to  pay  it.  The  transfer 
was  effected  by  a  qualified  indorsement. 
By  this  indorsement  Andrew  J.  Lloyd  avoids 
the  responsibility  of  an  ordinary  indorser. 

The  note  just  considered  is  a  time  note; 
if  the  words  On  demand  were  substituted 
for  the  words  Two  months  after  date  the  form 
would  be  called  a  demand  note.  The  note 
is  interest-bearing  because  it  contains  a 
clause  to  that  effect ;  it  would  draw  interest 
after  it  became  due  without  any  interest 
clause.  A  demand  note,  in  which  there  is 
no  interest  clause,  draws  interest  after  payment  has  been  demanded. 


Full  Indorsement 


Qualified  Indorsement 


310  PRACTICAL   BUSINESS   ARITHMETIC 

387.  A  note  in  which  two  or  more  persons  jointly  and 
severally  promise  to  pay  is  called  a  joint  and  several  note;  a 
note  in  which  two  or  more  persons  jointly  promise  to  pay,  a 
joint  note. 


Rochester,  MV  s^*.     .r        10 


after  date  we  jointly  and  severally  promise  to 


/ 

pay  totoi  order  of 

*^4£L^  2&s^*?^^^^f  "7s*-, .       .  Dollars 

Payable  at  — r^^ 
Value  received 


No. 


In  a  joint  and  several  note,  the  holder  may  sue  and  collect  of  any  one  signer 
without  proceeding  against  the  others,  or  he  may  sue  all  of  them  together. 
In  a  joint  note  the  signers  must  be  sued  jointly.  The  distinction  between 
a  joint  and  a  joint  and  several  note  has  been  .abolished  by  law  in  many  of 
the  states.  The  above  form  is  a  joint  and  several  note.  If  the  words  and 
severally  were  omitted  it  would  be  a  joint  note. 

The  words  value  received  in  a  note  are  equivalent  to  an  acknowledgment 
that  there  has  been  a  consideration.  Their  insertion  is  usual  and  advisable, 
but  not  legally  required  in  all  the  states. 

WRITTEN  EXERCISE 

Write  interest-bearing  notes  as  follows  : 

1.  A  demand  note;  amount,  §1283.97  ;  current  date;  payee, 
C.  H.  Good;  maker  (your  name);  interest  at  5J^. 

2.  A  time  note  ;  amount,  $  728.79  ;  current  date  ;  time,  90  da.  ; 
payee,  Snow  &  Co.;  maker  (your  name);  interest  at  3|  Jo. 

3.  A  joint  note;   amount,   11795.73;   current  date;  time,   6 
mo.;   payee,  Ellis  &   Co.;    maker    (your  name),  and  Richard 
Roe  ;  interest  at  4|  56.     Write  a  joint  note  under  the  same  con- 
ditions. 

4.  Find  the  amount  (face  plus  interest)  due  87  da.  after  date 
in  note  No.  1  ;    at  the  end  of  the  time  in  note  No.  2;  at  the 
end  of  the  time  in  note  No.  3. 


INTEREST  311 

EXACT   INTEREST 

388.  Exact  interest  is  simple  interest  for  the  exact  number  of 
days  on  the  basis  of  365  da.  in  a  common  year,  or  366  da.  in  a 
leap  year. 

The  United  States  Government  takes  exact  interest,  and  its  use  is 
growing  among  business  men.  In  strict  justice  it  is  the  only  correct 
method  of  computing  interest. 

389.  The   difference  between  the  common  year  of  365  da. 
and  the  commercial  year  of  360  da.  is  5  da.,  or  ^  of  the  com- 
mon year. 

If  any  sum  were  divided  into  360  parts,  each  part  would  be  larger  than  it 
would  be  if  the  sum  were  divided  into  365  parts.  Thus,  jfo  ail(i  sVo  are 
greater  than  jfo-  and  ^.  It  is  therefore  clear  that  exact  interest  is  less  than 
ordinary  interest. 

390.  To  find  the  exact  interest,  compute  interest  in  the  usual 
way  for  the  commercial  year,  and  from  the  interest  thus  obtained 
subtract  y^  of  itself. 

In  many  cases  the  work  may  be  shortened  by  cancellation. 

391.  Example.    Find  the  exact  interest  on  13285  for  35  da. 
at  5%. 

SOLUTION. 


WRITTEN  EXERCISE 
Find  the  exact  interest  : 

1.  $734.50  for  124  da.  at  6  %.     7.    $1240.35  for  50  da.  at  6%. 

2.  $420.60  for  99  da.  at  4J%.     8.    $1630.25  for  67  da.  at  4%. 

3.  $965.50  for  82  da.  at  3|  %.     9.    $150,000  for  28  da.  at  6%. 

4.  $356.40  for  236  da.  at  4%.   10.    $100,000  for  135  da.  at  5%. 

5.  $672.60  for  53  da.  at  5|%.  11.    $4653.28  for  182  da.  at  4%. 

6.  $546.24  for  38  da.  at  4|  %.  12.    $45,000  for  42  da.  at  21%. 

13.  $3500  from  July  17,  1907,  to  Nov.  26,  1907,  at  3%;  at  4|%. 

14.  $2315.89  from  Mar.  11,  1907,  to  Sept.  1,  1907,  at  6%  ;  at  2%. 

15.  $872.54  from  Oct.  18,  1906,  to  Jan.  16,  1907,  at  5  %  ;  at  7-|  %. 

16.  £  1006  6s.  from  Apr.  1,  1907,  to  Feb.  19,  1908,  at  3  %  ;  at  2  %  - 


312  PRACTICAL   BUSINESS   ARITHMETIC 

PROBLEMS   IN   INTEREST 

ORAL  EXERCISE 

1.  If  the  principal  is  $  100,  the  interest  $  12,  and  the  time  2 
yr.,  what  is  the  rate  ? 

2.  If  the  principal  is  $150,  the  interest  $18,  and  the  time 
3  yr.,  what  is  the  rate  ? 

3.  If  the  principal  is  $  200,  the  interest  $  24,  and  the  rate 
3  %,  what  is  the  time  ? 

4.  If  the  principal  is  $160,  the  interest  $12,   and  the  rate 

5  %,  what  is  the  time? 

5.  If  the  interest  is  $108,  the  rate  6%,  and  the  time  3  yr., 
what  is  the  principal  ? 

6.  If  the  interest  is  $42,  the  rate   3  %,  and  the  time   3  yr. 

6  mo.,  what  is  the  principal  ? 

7.  If  the  amount  is  $60,  the  rate  4%,  and  the  time  5  yr., 
what  is  the  principal  ? 

8.  When  the  cash  price  of  an  article  is  $  25,  what  should  the 
sixty-day  credit  price  be  ? 

9.  When  the  sixty-day  credit  price  of  an  article  is  $50.50, 
what  should  the  cash  price  be  ? 

10.  When   money    is    worth    5%,  what    cash    offer    will    be 
equivalent  to  a  ninety-day  credit  of  $101.25  ? 

11.  Which  is  the  better  and  how  much,  a  thirty-da}^  credit 
offer  of  $  100.50  or  a  cash  offer  of  $  98,  money  being  worth  6  %  ? 

12.  Which  is  the  better  and  how  much,  a  60-da.  credit  offer 
of  $404  or  a  casli  offer  of  $402,  money  being  worth  6%  ? 

13.  You  offer  a  customer  an  article  for  $  10  cash,  or  $  10.40 
on  4  mo.  credit.      If  you  consider  the  offers  equal,  how  much  is 
money  worth  to  you  at  the  present  time  ? 

14.  One  contractor  offers  to  do  a  certain  work  for  $  1050  cash ; 
another  offers  to  do  the  same  work  for  $  1075,  payable  in  1  yr. 
If  money  is  worth  7J%,  which  is  the  better  offer?  how  much 
better  ? 


INTEREST  313 

WRITTEN  EXERCISE 

1.  Which  is  the  better  for  a  tailor,  to  sell  a  suit  for  $65  cash, 
or  for  $73.15  on  9  mo.  time,  money  being  worth  6%  ? 

2.  Which  is  the  better,  to  sell  carpet  at  $1.50  per  yard  cash, 
or  at  $1.68  per  yard  on  1  yr.  time,  money  being  worth  5%  ? 

3.  Which  is  the  more  advantageous,  to  buy  an  article  for 
$58.50  cash  or  for  $61.80  on   6  mo.  time,   money  being  worth 
6%  ? 

4.  A  merchant  paid  $160  cash  for  4  sewing  machines.     After 
keeping  them  in  stock  1  yr.  6  mo.  he  sold  them  for  $190.80, 
on  one  year's  time  without  interest.     If  money  is  worth  6%  what 
was  his  gain  or  loss  ? 

5.  An  invoice  of  merchandise  listed  at  $2500,  on  which  trade 
discounts  of  20%  and  10%  were  allowed,  was  purchased  at  90 
da.     What  was  the  actual  cash  value  of  the  debt  on  the  day 
of  the  purchase,  money  being  worth  5  %  ? 

6.  A  merchant  bought  600  bbl.  of  flour  at  $7.50  per  barrel. 
Terms:    one  half  on  account,  3  mo.;  one  half  on  account,  6  mo. 
At  the  end  of  1  mo.  he  paid  the  cash  value  of  the  entire  bill. 
How  much  did  he  gain,  money  being  worth  6%? 

7.  Sept.  8  you  purchased  of  Edward  Sprague  &  Son,  at  trade 
discounts  of  20%  and  25%,  an  invoice  of  coffee  listed  at  $2006. 
Terms :  30  da.     Sept.  20  you  sent  Edward  Sprague  &  Son  a 
check  for  the  actual  cash  value  of  the  bill.     What  was  the 
amount  of  the  check,  money  being  worth  6%? 

PERIODIC   INTEREST 

392.  Periodic  interest  is  simple  interest  on  the  principal 
increased  by  the  simple  interest  on  each  installment  of  interest 
that  was  not  paid  when  due. 

As  periodic  interest  can  be  legally  enforced  in  only  a  few  states,  special 
contracts  should  be  made  if  it  is  to  be  collected.  Where  technically  illegal, 
periodic  interest  is  often  collected ;  as,  when  a  series  of  notes  is  given  for 
the  interest  on  a  note  secured  by  a  real-estate  mortgage,  such  notes  to  draw 
interest  if  not  paid  when  due. 


314  PRACTICAL   BUSINESS   ARITHMETIC 

393.  Example.    If  payments  of  interest  are  due  semiannually, 
what  is  the  interest  on  $1000  for  3  yr.  at  6%  ? 

SOLUTION 

$  180       =  interest  on  $  1000  for  3  yr.  at  6%. 

$30  is  the  interest  on  $  ]000  for  one  semiannual  period,  6  mo. 

1st  installment  of  interest,  $  30,  was  unpaid  for  2  yr.  6  mo. 

2d  installment  of  interest,  $  30,  was  unpaid  for  2  yr. 

3d  installment  of  interest,  $  30,  was  unpaid  for  1  yr.  6  mo. 

4th  installment  of  interest,  $  30,  was  unpaid  for  1  yr. 

5th  installment  of  interest,  $  30,  was  unpaid  for  6  mo. 

The  sum  of  the  periods  for  which  interest  was  unpaid  is     7  yr.  6  mo. 

The  interest  on  each  $30  for  the  period  it  was  unpaid  is  the  same  as 

the  interest  on  $30  for  the  sum  of  the  periods. 
13.50  =  interest  on  $30  for  7  yr.  6  mo.,  at  6%. 
$193.50  =  the  total  interest  due. 

WRITTEN   EXERCISE 

1.  If   payments    of  interest  are  due  annually,  what  is  the 
interest  on  $850  for  5  yr.,  at  8  %  ? 

2.  If  payments  of  interest  are  due  quarterly,  what  is   the 
interest  on  $1380  for  2  yr.  6  mo.,  at  4%? 

3.  What  is  the  difference  between  the  simple  interest  and 
periodic  interest  (payable  annually)  on  $1800  for  6  yr.  at  4%? 

4.  If  payments    of    interest    are    due    semiannually,    what 
amount  should  be  paid  in  settlement  of  a  debt  of  $1450  which 
has  run  5  yr.  at  6%? 

5.  If  payments  of  interest  are  due  annually,  what  amount 
will  settle  a  debt  of  $1500  for  5  yr.,  at  6%,  if  the  first  install- 
ment of  interest  was  paid  when  due? 

COMPOUND   INTEREST 

394.  Compound  interest  is  interest  computed,  at  certain  inter- 
vals, on  the  sum  of  the  principal  and  unpaid  interest. 

Interest  may  be  compounded  annually,  semiannually,  quarterly,  or  even 
monthly.  In  most  states  the  law  does  not  sanction  the  collection  of  com- 
pound interest,  but  if  it  is  agreed  upon  by  the  parties,  the  taking  of  it  does  not 
constitute  usury.  It  is  a  general  custom  of  savings  banks  to  allow  compound 
interest.  Compound  interest  is  also  used  by  life  insurance  companies. 


INTEREST 


315 


395.    Example.     What  is  the  compound   interest  on   $6000 
for  4  yr.,  if  the  interest  is  compounded  annually  at  5%? 

SOLUTION.   $  6000  =  1st  principal. 

300  =  interest  1st  year. 

6300  =  amount,  or  the  principal  the  2d  year. 

315  =  interest  2d  year. 

6615  =  amount,  or  the  principal  the  3d  year. 

330.75  =  interest  3d  year. 

6945.75  =  amount,  or  the  principal  the  4th  year. 

347.29  =  interest  4th  year. 

7293.04  —  amount  due  at  the  end  of  the  4th  year. 

$  7293.04  -  $  6000  =  $  1293.04,  compound  interest  for  4  yr. 

WRITTEN   EXERCISE 

1.  If  interest   is   compounded   annually,  what  will    be   the 
amount  of  1600  for  5  yr.  at  6  %  ? 

2.  If  interest  is  compounded  semiannually,  what  will  be  the 
compound  interest  on  $  1500  for  2  yr.  6  mo.  at  4  %  ? 

3.  A  man  deposited  $750  in  a  savings  bank  Jan.  1,  1905, 
and  interest  was  added  thereto  every  6  mo.  at  the  rate  of  4  %. 
No  withdrawals  having  been  made,  what  was  the  balance  due 
Jan.  1,  1907? 


11 

1.24337 

1.31209 

1.38423 

1.45997 

.53945 

1.62285 

1.71034 

11 

12 

1.26824 

.34489 

1.42576 

1.51107 

.60103 

1.69588 

1.79586 

12 

13 

1.29361 

.37851 

1.46853 

1.56396 

.66507 

1.77220 

1.88565 

13 

14 

1.31948 

.41297 

1.51259 

.61870 

.73168 

1.85194 

1.97993 

14 

15 

1.34587 

.44830 

1.55797 

.67535 

.80094 

1.93528 

2.07893 

15 

16 

1.37279 

.48451 

1.60471 

.73399 

1.87298 

2.02237 

2.18287 

16 

17 

1.40024 

.52162 

1.65285 

.79468 

1.94790 

2.11338 

2.29202 

17 

18 

1.42825 

.55966 

1.70243 

.85749 

2.02582 

2.20848 

2.40662 

18 

19 

1.45681 

1.59865 

1.75351 

.92250 

2.10685 

2.30786 

2.52695 

19 

20 

1.48595 

1.63862 

1.80611 

.98979 

2.19112 

2.41171 

2.65330 

20 

316  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

Refer  to  the  table,  page  315,  and  give  rapid  answers  to  the 
following  : 

l.    What  is  the  amount  of  $1  for  12  yr.  at  4%  ?  at  3%  ?  at 


5%?  at  4i%?  at  2| 

2.  What  is  the  amount  of  $1  for  18  yr.  at  4|%  ?  at 
at  2%  ?  at  3%  ?  at  2|  %  ? 

3.  What  is  the  amount  of  $1  for  9  yr.  at  5%  ?  at  4|%  ?  at 
21%  ?  at  3|%  ?  at  3%  ?  at  4%  ? 

4.  What  is  the  amount  of  $1  for  20  yr.  at  2%  ?  at  5%  ?  at 
4|%  ?  at  3|%  ?  at  2|%  ?  at  3%  ? 

5.  What  is  the  amount  of  1  10  for  10  yr.  at  4  %  ?  for  20  yr. 
at  2  %  ?  for  5  yr.  at  5  %  ? 

6.  What  is  the  amount  of  1100  for  5  yr.  at  2%  ?  for  11  yr. 
at  8J  %  ?  for  19  yr.  at  5  %  ? 

396.    Example.      What  is  the  compound  interest  on  $  8000 
for  10  yr.,  if  interest  is  compounded  annually  at  5%  ? 

SOLUTION.     $1.62889  =  amount  of  $1  for  10  yr.  at  5%. 

8000  x  $1.62889  =  $13031.12,  amount  due  in  10  yr.  at  5%. 
$13031.12  —  $8000  =  $5031.12,  the  compound  interest. 


1.  $7500  4%  5  yr.  Annually 

2.  $2500  2%  12  yr.  Annually 

3.  $5600  31%  20  yr.  Annually 

4.  $3350  5%  10  yr.  Semiannually 

5.  $2875  3%  17  yr.  Annually 

6.  $4600  4%  15  yr.  Semiannually 


INTEREST 


317 


SINKING  FUNDS 

397.  A  sinking  fund  is  a  sum  of  money  set  aside  at  regular 
intervals   for   the   payment  of   an  existing  or   anticipated  in- 
debtedness. 

The  payment  of  a  corporation  or  a  public  loan  is  sometimes  facilitated 
by  regularly  investing  a  certain  sum  in  some  form  of  security.  The  interest 
from  these  investments  from  year  to  year  constitutes  a  sinking  fund  which  it 
is  planned  shall  accumulate  to  an  amount  sufficient  to  redeem  the  debt  when 
it  falls  due. 

ORAL  EXERCISE 

1.  In  what  time  will  any  sum  of  money  double  itself  at  4  % 
simple  interest  ?  at  3  %  ?  at  6  %  ?  at  4-*  %  ? 

2.  How  long  (approximately)  will  it  take  $1  to  double  it- 
self at  3|%?  compound  interest,  compounded  annually?     (See 
table,  page  315.) 

3.  How  long  (approximately)  will  it  take  any  sum  to  double 
itself  at  4  J  %  compound  interest,  compounded  annually  ?  at  5  % 
compound  interest,  compounded  annually  ? 

4.  If  you  put  $1  at  compound  interest  to-day,  $1  one  year 
from  to-day,  and  so  on  for  20  yr.,  how  much  would  you  have 
at  the  end  of  the  twentieth  year,  interest  being  compounded 
annually  at  4J%  ?     (See  table  below.) 

398.  In  the  following  table  is  shown  the  amount  at  the  close 
of  a  series  of  years  of  $1  invested  at  different  rates  of  com- 
pound interest  at  the  beginning  of  each  year. 

COMPOUND  INTEREST  TABLE 


YR. 

2% 

4% 

44% 

YR. 

2% 

4% 

«|% 

1 

1.020000 

1.040000 

1.045000 

11 

12.412089 

14.025805 

14.464031 

2 

2.060400 

2.121600 

2.137025 

12 

13.680331 

15.626837 

16.159913 

3 

3.121608 

3.246464 

3.278191 

13 

14.973938 

17.291911 

17.932109 

4 

4.204040 

4.416322 

4.470709 

14 

16.293416 

19.023587 

19.784054 

5 

5.308120 

5.632975 

5.716891 

15 

17.639285 

20.824531 

21.719336 

6 

6.434283 

6.898294 

7.019151 

16 

19.012070 

22.697512 

23.741706 

7 

7.582969 

8.214226 

8.380013 

17 

20.412312 

24.645412 

25.855083 

8 

8.754628 

9.582795 

9.802114 

18 

21.840558 

26.671229 

28.063562 

9 

9.949721 

11.006107 

11.288209 

19 

23.297369 

28.778078 

30.371432 

10 

11.168715 

12.486351 

12.841178 

20 

24.783317 

30.969201 

32.783136 

318  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN  EXERCISE 

1.  At  the  beginning  of  each  year  for  10  yr.  a  certain  rail- 
road company  put  aside  out  of  the  profits  of  the  previous  year 
150,000  as  a  sinking  fund.      If  this  sum  was   invested  at  4% 
compound  interest,  compounded  annually,  what  did  it  amount 
to  at  the  end  of  the  tenth  year  ? 

2.  Jan.  1,  1907,  a  certain  city  borrowed  $500,000  and  agreed 
to  pay  the  principal  and  compound  interest,  compounded  annu- 
ally, at  4£%,  on  Jan.  1,  1917.     What  sum  must  be  invested  in 
securities,  paying  4|%  compound  interest,  compounded  annu- 
ally, on  Jan.  1,  1907,  and  annually  for  10  yr.,  in  order  to  pay 
the  loan  when  it  becomes  due  ? 

3.  On  Dec.  31,  1907,  a  certain  town  borrowed  $40,000  with 
which  to  build  a  new  high  school.     It  was   agreed  that  this 
amount  together  with  compound  interest,   compounded  annu- 
ally, at  4|%,  should  be  paid  on   Dec.   31,  1912.     What  sum 
must  the  town  set  aside  and  invest  at  4-|-%  compound  interest, 
compounded  annually,  on  Jan.  1,  1905,  and  each  year  there- 
after for  5  yr.,  in  order  to  pay  the  debt  when  it  becomes  due  ? 

WRITTEN  REVIEW  EXERCISE 

1.  What  amount  of  interest  (in  United  States  money)  at  6% 
will  accrue  on  a  debt  of  <£  84  12s.  in  5  mo.  24  da.? 

2.  The  yearly  taxes  on  a  house  and  lot  which  cost  $12,500 
are  $162.     How  much  should  the  house  rent  for  per  month 
to  clear  6%  on  the  investment  ? 

3.  A  Chicago  speculator  bought  16,000  bu.  of  wheat  at  85^, 
and  paid  for  it  in  10  da.     46  da.  from  the  date  of  purchase  he 
sold  the  wheat  for  92^  per  bushel,  cash.     If  money  was  worth 
4%,  what  did  he  gain? 

4.  A  savings  bank  account  was  opened  July  1,  1901,  with  a 
deposit  of  $800.     Interest  was  credited  every  6  mo.   at   4%. 
No  withdrawals  or  subsequent  deposits  having  been  made,  what 
was  the  balance  of  the  account  Jan.  1,  1907  ? 


INTEREST  319 

5.  The  note  on  page  308  was  not  paid  until  May  27.     How 
much  was  due  the  holder  of  the  note  on  that  date  ? 

6.  Jan.  1, 1905,  B  invested  124,000  in  a  manufacturing  busi- 
ness.    July  1,  1907,  he  withdrew  133,000,  which  sum  included 
the  original  investment  and   the   net   gains.     What   average 
yearly  per  cent  of  simple  interest  did  the  investment  yield  ? 

7.  Derby  &  Co.  offer  B  the  following  terms :  2/10,  N/30.    Jan.  1, 
B  bought  a  bill  of  goods  amounting  to  $ 4000  which  he  paid  Jan. 
31.     What  rate  of  interest  did  he  practically  pay  on  the  net 
amount  of  the  bill  by  not  taking  advantage  of  the  cash  offer  ? 

8.  In  a  certain  town  the  taxes  are  due  Sept.  15  of  each  year, 
and  all  taxes  unpaid  by  Oct.  15  are  subject  to  interest  from  the 
date  they  are  due,  at  6%.      The  following  taxes  were  paid  on 
the  dates  named:   Oct.  18,168.40;   Oct.  21,122.50;  Oct.  25, 
1132.75  ;  Oct.  31,  $98  ;  Nov.  11,  $176.80  ;  Nov.  23,  $326.30; 
Dec.  2,  $45  ;  Dec.  16,  $13.25  ;  Dec.  29,  $21.     How  much  in- 
terest was  paid,  the  time  being  the  exact  number  of  days  ? 

9.  Jan.  1,  1902,   F  bought   a   piece    of    city   property   for 
$20,000,  paid  cash  $4000,  and  gave  a  note  and  mortgage  for 
5  yr.  without  interest,  to  secure  the  balance.     To  cover  the  in- 
terest, which  it  was  agreed  should  be  met  quarterly,  he  gave 
twenty  notes  for  $240  each,  one  maturing  every  three  months. 
The  first  five  installments  of  interest  were  paid  when  due,  and  the 
balance  of  the  mortgage  and  the  interest  were  paid  Jan.  1, 1907. 
Find  the  final  payment. 

10.  Lester  B.  Ford  keeps  his  deposit  with  the  Second  National 
Bank,  and  has  left  with  the  bank  railroad  stock  valued  at  $1000 
as  collateral  security  for  overdrafts,  the  bank  charging  5  %  on 
all  overdrafts  that  were  not  settled  within  3  da.     May  6  there 
was  an  overdraft  of  $280  that  was  settled  May  13;  May  28, 
$312.50,  that  was  settled  June  1;  June  26,  $156.75,  that  was 
settled  July  8 ;  Aug.  1,  $456.20,  that  was  settled  Aug.  11.    How 
much  interest  did  Mr.  Ford  have  to  pay  ? 


CHAPTER   XXVI 

BANK  DISCOUNT 
ORAL  EXERCISE 

1.  What  is  meant  by  a  promissory  note  ?  by  the  face  of  a 
note  ?  by  the  time  ?  by  the  maker  ?  by  the  payee  ? 

2.  How  would  you  word  a  promissory  note  for  $600,  dated 
at  your  place  to-da}7,  payable  in  60  da.  at  a  bank  in  your  place, 
with  interest  at  5%,  to  C.  B.  Powell,  signed  by  yourself? 

3.  What   is    meant   by   negotiable  ?  by    indorsing   a   note  ? 
Illustrate  a  blank  indorsement  ;    an  indorsement  in  full  ;    a 
qualified  indorsement. 

399.  A  commercial  bank  is  an  institution  chartered  by  law  to 
receive  and  loan  money,  to  facilitate  the  transmission  of  money 
and  the  collection  of  negotiable  paper,  and,  in  some  cases,  to 
furnish  a  circulating  medium. 

400.  If  the  holder  (owner)  of  a  promissory  note  wishes  to 
use  the  money  promised  before  it  becomes  due,  a  commercial 
bank  will  usually  buy  the  note,  provided  the  holder  can  show 
that  it  will  be  paid  at  maturity,   that  is,  when  it  becomes  due. 
This  is  called  discounting  the  note. 

j£jL£^==-  New  Y™*,          //Z^gzsrs  /# .       M 

-pay  to 


BANK   DISCOUNT  321 

401.  A  commercial  draft  is  now  frequently  used,  instead  of 
the  promissory  note,  as  security  for  the  payment  of  goods  sold 
on  credit.  Such  a  draft  may  be  defined  as  a  written  order  in 
which  one  person  directs  another  to  pay  a  specified  sum  of 
money  to  the  order  of  himself  or  to  a  third  person. 

The  circumstances  under  which  the  foregoing  draft  was  drawn  are  as 
follows:  Geo.  H.  Catchpole  sold  Frank  G.  Hill  goods  amounting  to  $460.80. 
Terms :  30-da.  draft.  The  draft  and  an  invoice  were  made  out  and  sent 
to  Frank  G.  Hill  by  mail.  Frank  G.  Hill  accepted  the  draft,  that  is,  signi- 
fied his  intention  to  pay  it  by  writing  the  word  accepted,  the  date,  and  his 
name  across  the  face.  The  draft  was  then  returned  to  Geo.  H.  Catchpole, 
who  may  discount  it  the  same  as  lie  would  an  ordinary  promissory  note. 

The  parties  to  a  draft  are  the  drawer,  the  drawee,  and  the  payee.  In  the 
foregoing  draft,  George  II .  Catchpole  is  both  the  drawer  and  the  payee, 
and  Frank  G.  Hill  is  the  drawee. 

A  draft  payable  after  sight  begins  to  mature  from  the  date  on  which  it  is 
accepted.  An  acceptance  must,  therefore,  be  dated  in  a  draft  payable  after 
sight,  but  it  may  or  may  not  be  dated  in  a  draft  payable  after  date. 


Some  states  allow  three  days  of  grace  for  the  payment  of  notes  and  other 
negotiable  paper.  Days  of  grace  are  obsolete  in  so  many  of  the  states  that 
they  are  not  considered  in  the  exercises  in  this  book.  Some  states  provide 
that  when  paper  matures  on  Sunday  or  a  legal  holiday  it  must  be  paid  the 
day  preceding  such  Sunday  or  legal  holiday ;  others  provide  that  it  must  be 
paid  on  the  day  following.  To  hold  all  interested  parties,  the  laws  of  any 
given  state  should  always  be  observed.  When  the  time  of  negotiable  paper 
is  expressed  in  months,  calendar  months  are  used  to  determine  the  date  of 
maturity ;  but  when  the  time  is  expressed  in  days,  the  exact  number  of  days 
is  used.  Thus,  a  note  payable  2  mo.  after  July  15  is  due  Sept.  15 ;  but  a 
note  payable  60  da.  after  July  15  is  due  Sept.  13.  Paper  payable  1  mo. 
from  May  31,  Aug.  31,  etc.,  is  due  Jan.  30,  Sept.  30,  etc. 


322 


PRACTICAL   BUSINESS  ARITHMETIC 


MATURITY  TABLE 


402.  The  time  from  the  date  of  discount  to  the  maturity  of 
paper  is  called  the  term  of  discount ;  the  whole  sum  specified  to 
be  paid  at  maturity,  the  value,  or  amount,  of  the  paper. 

The  term  of  discount  is  usually  the  exact  number  of  days  from  the  date  of 
discount  to  the  date  of  maturity.  Some  banks,  however,  find  the  term  of 
discount  by  compound  subtraction,  and  then  reduce  the  time  to  days;  e.g. 
the  term  of  discount  on  a  note  due  May  6  and  discounted  Mar.  1  is  counted 
as  2  mo.  5  da.,  or  65  da.  In  this  text  the  term  of  discount  is  the  exact  number 
of  days  from  the  date  of  discount  to  the  maturity  of  the  paper. 

403.  The  reduction  made  by  a  bank  for  advancing  money  on 
negotiable  paper  not  due  is  called  bank 

discount.  The  value  of  negotiable  paper 
at  maturity,  minus  the  bank  discount,  is 
called  the  proceeds. 

Bank  discount  is  always  the  simple  interest  for 
the  term  of  discount  on  the  whole  sum  specified  to 
be  paid  at  maturity. 

404.  The  accompanying  maturity  table 
is  sometimes  used  by  bankers  in  finding 
the  maturity  of  notes  and  drafts.     The 
following  examples  illustrate  its  use. 

405.  Examples.   1.    Find   the   maturity 
of  a  note  payable  (#)  6  mo.  from  Apr.  27, 
1906 ;   (6)  6  mo.  from  Sept.  25,  1906. 

SOLUTIONS,  (a)  Referring  to  the  table,  observe 
that  April  is  the  4th  month;  adding  4  and  6,  the 
result  is  10,  and  the  10th  month  (see  number  on  left) 
is  October.  The  note  is  therefore  due  Oct.  27,  1906. 

(&)  September  is  the  9th  month.  9  +  6  =  15,  and  the  15th  month  (see  number 
oh  right)  is  March  of  the  next  year.  The  note  is  therefore  due  Mar.  25,  1907. 

2.  Find  the  maturity  of  a  note  payable  90  da.  from  Jan.  18, 
1907. 

SOLUTION.  1  +  3  =  4,  and  the  4th  month  is  April.  If  the  note  were  pay- 
able in  3  mo.,  it  would  be  due  Apr.  18.  Referring  to  the  table,  note  that  2 
da.  (1  da.  +  1  da.)  must  be  subtracted  for  January  and  March,  and  2  da.  added 
for  February.  The  note  is  therefore  due  Apr.  18. 

After  the  student  has  become  familiar  with  the  principles  of  the  table  it  will 
not  be  found  necessary  to  consult  it. 


1 

Jan.  —  1 

13 

2 

Feb.  +  2 

14 

3 

Mar.  -  1 

15 
16 

4 

Apr. 

5 

May-  1 

17 

6 

June 

18 

7 

July  -  1 

19 

8 

Aug.  -  1 

20 

9 

Sept. 

21 

10 

Oct.  -  1 

22 

11 

Nov. 

23 

12 

Dec.  -  1 

24 

BANK  DISCOUNT  323 

ORAL   EXERCISE 

Find  the  maturity  of  each  of  the  following  notes  : 

DATE  TIME  DATE  TIME 

1.  Apr.  6,  1906  30  da.  6.  Jan.  30,  1907  30  da. 

2.  Oct.  6,  1907  3  mo.  7.  Jan.  31,  1906  30  da. 

3.  Nov.  9,  1906  60  da.  8.  May  10,  1907  90  da. 

4.  Jan.  31,  1907  1  mo.  9.  June  19,  1907  60  da. 

5.  Sept.  18,  1906  90  da.  10.  Nov.  15,  1907  30  da 

Find  the  maturity  of  each  of  the  following  acceptances  : 

n  TIME  AFTER  TIATW  TIME  AFTER 

DATE  DATE 

11.  Apr.  3  30  da.  14.    Dec.  31  2  mo. 

12.  May  5  60  da.  15.    Jan.  12  1  mo. 

13.  Jan.  29  1  mo.  16.    Feb.  18  3  mo. 
Find  the  maturity  of  each  of  the  following  acceptances: 

DATE  TIME  AFTER  DATE  TIME  AFTER 

ACCEPTED  SIGHT  ACCEPTED  SIGHT 

17.  Aug.  12  3  mo.  20.    Apr.  25          60  da. 

18.  Sept.  18  2  mo.  21.    May  17  3  mo. 

19.  Oct.    30  4  mo.  22.    June  18          30  da. 

WRITTEN   EXERCISE 

Find  the  maturity  and  the  term  of  discount: 

DATE  TIME  DISCOUNTED 

1.  Jan.  16,  1907  3  mo.  Mar.  1 

2.  Jan.  31,  1907  1  mo.  Feb.  3 

3.  Feb.  12,  1907  90  da.  Mar.  2 

4.  Feb.  24,  1907  60  da.  Apr.  1 

.       5.    Mar.  31,  1907  90  da.  May  13 

DATE  OF  DRAFT       TIME  AFTER  DATE       DATE  ACCEPTED    DATE  DISCOUNTED 

6.  Feb.   7  60  da.  Feb.    8  Feb.    9 

7.  Mar.  12  30  da.  Mar.   12  Mar.  15 

DATE  OF  DRAFT       TIME  AFTER  SIGHT       DATE  ACCEPTED    DATE  DISCOUNTED 

8.  May  31  60  da.  May  31  June  3 

9.  Mar.  17  90  da.  Mar.  20  Mar.  21 


324 


PRACTICAL   BUSINESS   ARITHMETIC 


406.    The  following  time  table  is  frequently  used  by  bankers 
in  finding  the  exact  number  of  days  between  any  two  dates : 


TABLE  OF  TIME 


FROM  ANY  DAY 

OF 

To  THE  SAME  DAY  OF  THE  NEXT 

Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

151 
120 
92 
61 
31 
365 
335 
304 
273 
243 
212 
182 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

JANUARY  .... 
FEBRUARY  .  .  . 
MARCH  .... 
APRIL 

365 
334 
306 
275 
245 
214 
184 
153 
122 
92 
61 
31 

31 
365 
337 
306 
276 
245 
215 
184 
153 
123 
92 
62 

59 
28 
365 
334 
304 
273 
243 
212 
181 
151 
120 
90 

90 
59 
31 
365 
335 
304 
274 
243 
212 
182 
151 
121 

120 
89 
61 
30 
365 
334 
304 
273 
242 
212 
181 
151 

181 
150 
122 
91 
61 
30 
365 
334 
303 
273 
242 
212 

212 
181 
153 
122 
92 
61 
31 
365 
334 
304 
273 
243 

243 
212 
184 
153 
123 
92 
62 
31 
365 
335 
304 
274 

273 
242 

214 
183 
153 
122 
92 
61 
30 
365 
334 
304 

304 
273 
245 
214 
184 
153 
123 
92 
62 
31 
365 
335 

334 
303 
275 
244 
214 
183 
153 
122 
91 
61 
30 
365 

MAY 

JUNE  

JULY 

AUGUST  .... 
SEPTEMBER  .  .  . 
OCTOBER  .... 
NOVEMBER  .  .  . 
DECEMBER  .  .  . 

The  exact  number  of  days  from  any  day  of  any  month  to  the  correspond- 
ing day  of  any  other  month,  within  a  year,  is  found  in  the  column  of  the 
last  month  directly  opposite  the  line  of  the  first  month.  Thus,  from  June 
6  to  Sept.  6  is  92  da. ;  from  Apr.  1  to  Oct.  1  is  183  da. ;  from  Aug.  26  to 
Dec.  26  is  122  da.  The  exact  number  of  days  between  any  two  dates  is 
found  as  in  the  following  illustrations : 

407.    Examples.    1.    How  many  days  from  Mar.  1  to  May  11  ? 

SOLUTION.  From  Mar.  1  to  May  1  is  61  da.  From  May  1  to  May  11  is  10 
da.  61  da.  -f  10  da.  =  71  da.,  the  required  result. 

2.    How  many  days  from  July  26  to  Oct.  6  ? 

SOLUTION.  From  July  26  to  Oct.  26  is  92  da.  From  Oct.  26  back  to  Oct.  6 
is  20  da.  92  da.  -  20  da.  =  72  da.,  the  required  result. 

ORAL  EXERCISE 

By  the  table  find  the  exact  number  of  days  from : 

1.  July  8  to  Sept.  8.  7.    May  31  to  Aug.  1. 

2.  Jan.  6  to  Mar.  6.  8. 

3.  Jan.  23  to  June  23.  9. 

4.  Feb.  13  to  July  13.  10. 

5.  Mar.  11  to  Sept.  11.  11. 

6.  Mar.  21  to  Aug.  21.  12. 


Feb.  23  to  Sept.  23. 
Mar.  24  to  July  12. 
May  11  to  Aug.  31. 
Aug.  15  to  Dec.  10. 
Nov.  25  to  Mar.  25. 


BANK   DISCOUNT 


325 


408.  Examples,     l.    Find  the  proceeds  of  a  note  for  13000, 
payable  in  78  da.,  discounted  at  6%. 

SOLUTION.     $0.013  =  the  rate  for  the  term  of  discount. 
3000  x  $0.013  =  $39,  the  bank  discount. 
$3000  -  $39  =  $2961,  the  proceeds. 

2.  A  note  for  -16000  payable  in  60  da.  from  May  10,  1907, 
with  interest  at  6%,  is  discounted  May  25,  at  6%.  Find  the 
maturity,  the  term  of  discount,  the  bank  discount,  and  the 
proceeds. 

SOLUTION.     July  9,  1907  =  the  maturity. 

45  da.  =  the  term  of  discount. 

.$60  =  the  interest  on  the  note  for  60  da. 
$6060  =  the  value  of  the  note  at  maturity. 
$  45.45  =  the  bank  discount. 
$6014.55  =  the  proceeds. 

409.  The    accompanying   diagram    illustrates  *a    convenient 
outline  for  learning  the  proper 

method  of  computing  bank  dis- 
count. It  will  be  observed  that 
the  first  problem  is  an  interest- 
bearing  note,  and  the  second 
problem  a  non-interest-bearing 
note.  The  items  in  black  ink 
are  taken  from  the  problem,  and 
the  items  in  red  ink  are  found 
as  previously  explained. 


&</. 


f-303 
f/.j-a. 


WRITTEN   EXERCISE 

1.  Assuming  that  the  model  note,  page  9,  was  discounted 
July  2,  at  6%,  find  the  bank  discount  and  the  proceeds. 

2.  Assuming  that  the  model  note,  page  308,  was  discounted 
Jan.  20,  at  6%,  find  the  bank  discount  and  the  proceeds. 

3.  Assuming  that  the  model  note,  page  310,  was   discounted 
Aug.  26,  at  6  %,  find  the  bank  discount  and  the  proceeds. 

4.  Assuming  that  the  model  draft,  page  320,  was  discounted 
May  15,  at  6  % ,  find  the  bank  discount  and  the  proceeds. 


326  PRACTICAL   BUSINESS    ARITHMETIC 

5.  Assuming  that  the  model  draft,  page  321,  was  discounted 
April  12,  at  6%,  find  the  bank  discount  and  the  proceeds. 

6.  Find  the  proceeds  of  the  following  joint  note: 
§895.40  BALTIMORE,  MD.,  May  25,  1907. 

Six  months  after  date,  for  value  received,  we  promise  to  pay 
to  the  order  of  Ralph  D.  Gibson  Eight  Hundred  Ninety-rive 
-f^Q  Dollars,  at  Exchange  National  Bank. 

SETH  M.  BULLARD. 
Discounted  July  2,  1907,  at  5%.  ISAAC  C.  AV  ATKINS. 

7.  Find  the  proceeds  of  the  following  joint  and  several  note: 
$  1000.00  COLUMBUS.  O..  May  1.  1907. 

Three  months  after  date  we  jointly  and  severally  promise  to 
pay  to  the  order  of  Wilson  N.  Burton  One  Thousand  Dollars, 
at  Second  National  Bank,  Columbus,  O.,  with  interest  at  6%. 

Value  received.  JOHN  M.  SELLERS. 

Discounted  June  2,  1907,  at  6%.          DANIEL  W.  SHELDON. 

8.  Find  the  proceeds  of  the  following  firm  note: 
81250.00  ST.  Louis.  Mo..  Aug.  -20.  1907. 

Ninety  days  after  date  we  promise  to  pay  to  the  order  of 
C.  M.  Courtwright  Twelve  Hundred  Fifty  Dollars,  at  the 
National  Bank  of  Redemption,  with  interest  at  5%. 

Value  received.  J.  M.  Cox  &  SON. 

Discounted  Sept.  1,  1907,  at  6%. 

9.  Sept.  26  you  sold  R.  M.  Stein,  Portland,  Me.,  a  bill  of 
hardware  amounting  to  *  2-180,  less  20  %,  25  %,  and  10  % .   Terms : 
\  by  60-da.  note  with  interest  at  6  %  ;  \  on  account  60  da.    What 
was  the  amount  of  the  note  which  was  this  day  received? 

10.  Oct.  12  you  discounted  at  Union  Bank,  at  6%,  R.  M. 
Stein's  note  received  Sept.  26,  the  bank  giving  you  credit  for 
the  proceeds.  If  the  bank  charges  -^  %  for  collecting  out-of- 
town  paper,  what  was  the  amount  of  the  proceeds  credited  ? 

A  small  fee  called  collection  and  exchange  is  sometimes  charged  on 
discounted  paper  payable  out  of  town.  The  charge  is  by  no  means 
uniform,  being  controlled  largely  by  the  size  of  the  depositor's  account  and 
the  general  custom  of  the  banks  in  any  given  locality. 


BANK   DISCOUNT 


B27 


11.  The  following  is  a  part  of  a  page  from  a  bank's  discount 
register.  Copy  it,  supplying  all  missing  terms.  The  notes 
were  all  discounted  June  17. 


So. 

DATE  <>K 
PAIT.K 

TIME 

WIIEX 
DIE 

TERM  OF 

I)!-i  <U  NT 

BATE  OF 
DISCOUNT 

VALUE  OF 
PAPER 

Disc. 

COLL.  & 
Exce. 

PROCEEDS 
CREDITED 

20 

Apr.  25 

3  mo. 

6% 

2000 

00 

21 

May  1 

3  mo. 

6% 

3500 

00 

3 

50 

2-2 

Apr.  1 

90  da. 

6% 

1500 

00 

23 

Apr.  15 

90  da. 

6% 

900 

60 

•J4 

June  15 

30  da. 

6% 

378 

90 

38 

12.  Sept.  15  the  First  National  Banb  notifies  you  that  your 
bank  account  is  overdrawn  §1725.90.     You  immediately  offer 
for  discount,  at  6%,  the  following  notes,  the  proceeds  of  which 
are  to  be  placed  to  your  credit :     E.  M.  Robinson's  30-day  note 
dated  Sept.  1,  for  § 300;  C.  E.  Reardon's  note  payable  3  mo. 
from  July  25,  with  interest  at  6  %,  for  $427.65;  C.  W.  Allen's 
60-day  note  dated  Aug.  1,  for  §321.17;  F.  H.  Clark's  60-day 
note  dated  July  30,  for  §1500.     What  is  your  credit  at  the  bank 
after  discounting  the  notes? 

13.  Apr.  6,  1907,  Peter  W.  Berger  has  on  deposit  in  the 
First  National  Bank  §523.87.     He  draws  a  check  for  $1176.45, 
and   then   discounts   the  following  notes  at  the  bank,  at  6%, 
receiving  credit  for  the  proceeds.     What  was  the  balance  of  his 
account  after  the  notes  were  discounted  and  credited? 

a. 

8  346. 50  HARTFORD,  CONN.,  Mar.  1, 1907. 

Ninety  days  after  date  I  promise  to  pay  Peter  W.  Ber- 
ger, or  order,  Three  Hundred  Forty-six  -ffo  Dollars,  at  First 
National  Bank,  Hartford,  Conn. 

Value  received.  HENRY  S.  LANE. 

b. 
§575.00  HARTFORD,  CONN.,  Feb.  1,  1907. 

Aug.  1,  1907,  I  promise  to  pay  Peter  W.  Berger,  or  order, 
Five  Hundred  Seventy-five  Dollars,  at  Second  National  Bank, 
Hartford,  Conn. 

Value  received.  SAMUEL  D.  SKIFF. 


328 


PRACTICAL   BUSINESS    ARITHMETIC 


14.  July  18,  C.  B.  Snow's  bank  balance  is  1312.90.  He  dis- 
counts at  6  %  the  following  drafts,  and  then  issues  a  check  in 
payment  for  5  sewing  machines  at  175,  less  20%  and  25%. 
What  is  the  amount  of  his  balance  after  issuing  the  check? 


a. 


^L 19— 


sS^£. 


J^b£^&s*.^j«  .*'/~ 


'Dollar 


Value  receioed 


flfr.  2,  rPue 


BANK  LOANS 

410.  The  foregoing  exercises  have  reference  to  paper  bought 
or  discounted  by  a  bank.  Money  is  frequently  loaned  upon 
the  notes  of  the  borrower,  indorsed  by  some  one  of  known 
financial  ability,  or  secured  by  the  deposit  of  stocks,  bonds, 
warehouse  receipts,  or  other  collaterals.  These  notes,  if  drawn 
on  time,  are  not  interest-bearing,  but  the  bank  discounts  them 
by  deducting  from  their  face  the  interest  for  the  full  time. 


BANK   DISCOUNT  329 

411.  Loans  are  sometimes  made  on  call  or  demand  notes  ;  that 
is,  on  notes  that  can  be  called  or  demanded  at  any  time  after 
they  are  made.  These  notes  are  interest-bearing  and  are  drawn 
for  the  exact  sum  loaned. 

Call  or  demand  loans  generally  bear  a  lower  rate  of  interest  than  loans  on 
time.  They  are  made  principally  to  brokers  and  speculators,  who  use  them 
to  pay  for  stocks  ;  but  they  are  also  made  to  merchants  and  others  to  some 
exte.nt.  Business  men,  however,  generally  prefer  to  borrow  on  time,  for 
they  do  not  wish  to  be  embarrassed  by  having  the  loans  called  in  at  an 
unexpected  time.  Time  loans  are  usually  drawn  for  thirty,  sixty,  or  ninety 
days.  If  the  borrower  requires  money  for  a  longer  period,  the  bank  will 
usually  allow  him  to  renew  the  note  when  it  falls  due. 

WRITTEN  EXERCISE 

1.  Jan.  7,  1907,  E.  L.  Jennings  &  Co.  desire  to  extend  their 
business,  and  for  this  purpose  borrow  money  at  6  %  of  the  First 
National  Bank  of  New  York,  on  the  following  note.  How 
much  will  the  bank  place  to  the  credit  of  E.  L.  Jennings  &  Co.  ? 


19  _ 


fff  Jate^£tSZ/-f>romt»e  to  pay  to 


Value  received 

^^7^^^y^f  ¥^~V?^rx' 


2.  You  gave  the  Union  National  Bank,  of  your  city,  your 
note,  for  11200,  at  60  da.,  indorsed  by  Williams  &  Rogers. 
How  much  cash  will  the  bank  advance  you,  if  discount  is 
deducted  at  the  rate  of  6% 


3.  Howe  &  Rogers,  Buffalo,  N.Y.,  borrowed  112,000  of  Mer- 
chants National  Bank  on  their  demand  note  secured  by  300 
shares  of  Missouri  Pacific  Railway  stock,  at  $50.  If  the  rate 
of  interest  was  21%,  how  much  was  required  for  settlement 
39  da.  after  the  loan  was  made  ? 


330  PRACTICAL   BUSINESS   ARITHMETIC 

4.  Jan.  1,  1906,  C.  W.  Allen  &  Co.,  brokers,  borrowed  of 
First  National  Bank,  Boston,  Mass.,  $15,000  on  the  following 
collateral  note.  How  much  was  required  for  full  settlement 
of  the  loan  57  da.  after  it  was  made  ? 


Boston,  Mn«  ^^-.   2.  _  19  _ 

fnr  value  received,  ~-£tsz~  promise  to  pay  to  the  order  of 
f^  at  their  banking  house 

^r>  -  -------          -  Dollars 


As  collateral  security  tor  the  payment  of  the  note  and  all  other  liabilities  to  said  bank,  either  absol 
contingent,  now  existing  or  to  be  hereafter  incurred,  -44/T-  have  deposited  with  it  : 


Should  the  market  value  of  the  same  decline,  -^Ur&-  promise  to  furnish  satisfactory  additional  collateral  on 
demand,  which  may  be  made  by  a  notice  in  writing,  sent  by  mail  or  otherwise,  to  (T^^  residence  or  place  of 
business.  On  the  nonperformance  of  either  of  the  above  promises  -usr^  authorize  the  holder  or  holders 
hereof  to  sell  said  collateral  and  any  collaterals  added  to  or  substituted  for  the  same,  without  notice,  at  public  or 
private  sale,  and  at  or  before  the  maturity  hereof,  he  or  they  giving  -4*^d-  credit  for  any  balance  of  the  net 
proceeds  of  such  sale  remaining  after  paying  all  sums  absolutely  or  contingently  due  and  then  or  thereafter 
payable  from  -£«<£-  to  said  holder  or  holders.  And  ~WZ-  authorize  said  holder  or  holders,  or  any  person  in 
his  or  their  behalf,  to  purchase  at  any  such  sale. 


FINDING   THE    FACE 

412.  Example.  I  wish  to  borrow  $1980  of  a  bank.  For 
what  sum  must  I  issue  a  60-cla.  note  to  obtain  the  amount,  dis- 
count being  at  the  rate  of  6%  ? 

SOLUTION.  Let  the  face  of  the  note  =  $  1 

Then  the  bank  discount  =  $0.01 
And  the  proceeds  =  80.99 

But  the  proceeds  =  $  1980 

$1980 -$0.99  =     2000 

/.  the  face  of  the  note  is  2000  x  $1,  or  §2000. 

WRITTEN   EXERCISE 

1.  What  must  be  the  face  of  a  30-da.  note  in  order  that  when 
discounted  at  6  %  the  proceeds  will  be  1 1990  ?  Of  a  60-da.  note, 
same  conditions? 

2.  You  wish  to  borrow  13940  cash.     What  must  be  the  face 
of  a  90-da.  note  in  order  that  when  discounted  at  6  %  the  pro- 
ceeds will  be  the  required  sum? 


; 


BANK   DISCOUNT 


331 


3.  Oct.  15,  J.  M.  King  bought  of  you  goods  amounting  to 
13500,  less  20%   and    10%.     Terms:    cash.     Not  having  the 
money,  he  gave  you  his  60-da.    note,  dated   Oct.   15,  for  an 
amount  equivalent  to  the  cash  value  of  the  goods.     What  was 
the  face  of  the  note,  money  being  worth  6%  ? 

4.  You  purchased  through  W.  D.  Allen,  an  agent,  3000  Ib. 
coffee  at  33J^.     Commission  3%;   guaranty  2%.  -  You  gave 
Mr.  Allen  a  30-da.    note,  which  when  discounted  at  6%  for 
its  full  term  just  covered  the  amount  due.     If  the  note  bore 
interest  at  5%,  what  was  its  face? 


WRITTEN  REVIEW  EXERCISE 

1.  Find   the   proceeds  of    the    following    note,     discounted 
Feb.  2  at  5%  ;   collection  charges  |%. 

12700.00  Los  ANGELES,  CAL.,  Dec.  27,  1906. 

Mar.  27,  1907,  we  promise  to  pay  to  the  order  of  F.  M.  Dun- 
bar  &  Son  Twenty- seven  Hundred  Dollars,  at  the  Union  Bank 
of  Los  Angeles,  with  interest  at  4  % . 

Value  received.  GRAY  &  SALISBURY. 

2.  Copy  the  following  discount  memorandum,  supplying  all 
missing  terms : 


FIRST  NATIONAL  BANK 


Boston,  Mass., 


(L 


10 


ybrUrZ-O 

2-e 
20 
2-0 


/2-fV<&, 
/* 


/J" 


t 


tftf 


CHAPTER   XXVII 

PARTIAL  PAYMENTS 
THE   UNITED   STATES   METHOD 
ORAL  EXERCISE 

1.  A  note  for  $500  bears  interest  at  6%.      What  amount 
would  pay  the  note  and  interest  at  the  end  of  1  yr.  ? 

2.  Suppose  that  a  payment  of  $130  was  made  at  the  end  of 
1  yr.     After  the  accrued  interest  has  been  paid,  how  much  is 
there  left  to  apply  to  the  face  of  the  note  ? 

3.  After  the  $100  has  been  applied  to  the  face  of  the  note, 
what  amount  does  the  maker  continue  to  keep?     On  what  sum, 
therefore,  should  he  pay  interest  after  the  first  year  ? 

4.  The  maker  kept  the  remaining  $400  another  year.      How 
much  interest  was  then  due  ?     What  was  the  total  amount  due  ? 

5.  If  a  payment  of  $224  was  made  at  this  time,  what  amount 
still  remained  unpaid  ?     If  the  balance  of  the  note  was  paid 
three  years  after  it  was  issued,  what  was  the  amount  of  the 
payment  ? 

413.  Partial  payments  are  payments  in  part  of  a  note  or  bond. 
Such  payments  may  be  made  either  before  or  after  maturity.     They 

should  be  acknowledged  by  indorsement  on  the  back  of  a  note  or  bond. 
Current  forms  for  indorsing  partial  payments  on  notes  are  illustrated  on 
page  336. 

414.  The  United  States  method  of  partial  payments  (as  sug- 
gested in  problems  1-5  above)  has  been  adopted  by  the  Supreme 
Court  of  the  United  States,  and  made  the  legal  method  in  nearly 
all  the  states. 

This  is  the  method  ordinarily  used  by  individuals  when  the  time  between 
the  date  of  the  note  and  its  payment  is  more  than  one  year. 

332 


PARTIAL   PAYMENTS 


333 


415.  Example.  A  note  for  11200,  dated  Jan.  1,  1906,  bear- 
ing interest  at  6%,  had  payments  indorsed  upon  it  as  follows  : 
Mar.  1,1906,  $212;  July  1,  1906,  1 15;  Sept.  1,1906,1515; 
Nov.  1,  1906,  $175.  How  much  was  due  upon  the  note  at  final 
settlement,  Apr.  1,  1907  ? 

SOLUTION 

Face  of  note $1200. 

Interest  from  Jan.  1,  1906,  to  Mar.  1,  1906  (2  mo.)  ...  12. 

Amount  due  Mar.  1,  1906 1212. 

Payment  Mar.  1,  1906 212. 

New  principal,  or  amount  to  draw  interest  after  Mar.  1,  1906  .  1000. 

Interest  from  Mar.  1,  1906,  to  July  1,  1906  (4  mo.)          .         .          $20. 
Interest  exceeds  the  payment  and  the  principal  remains  unaltered. 
Interest  from  July  1,  1906,  to  Sept.  1,  1906  (2  mo.)          .         .          $10. 

Total  interest  due  Sept.  1,  1906          . ~~          30. 

Amount  due  Sept.  1,  1906 

Sum  of  the  payments  since  July  1  ($15 -f$  51 5)        .... 
New  principal,  or  amount  to  draw  interest  after  Sept.  1,  1906 
Interest  from  Sept.  1,  1906,  to  Nov.  1,  1906  (2  mo.) 

Amount  due  Nov.  1,  1906 

Payment  Nov.  1,  1906  

New  principal,  or  amount  to  draw  interest  after  Nov.  1,  1906  .  330. 

Interest  from  Nov.  1,  1906,  to  Apr.  1,  1907  (5  mo.)  .        .         .  8.25 

Amount  due  at  settlement,  Apr.  1,  1907  .         ...         .         $338.25 

It  will  be  observed  in  the  foregoing  example  that  the  United  States  method 
provides  :  (1)  that  the  payment  must  first  be  applied  to  discharge  the  accrued 
interest ;  (2)  that  the  surplus,  if  any,  after  paying  the  interest  may  be  used  to 
diminish  the  principal;  and  (3)  that  if  any  payment  is  less  than  the  accrued 
interest,  the  principal  remains  unaltered  until  some  payment  is  made  with  which 
the  preceding  neglected  payment  or  payments  is  more  than  sufficient  to  discharge 
the  accrued  interest, 

CONDENSED  FORM   FOR   WRITTEN   WORK 


1030. 
530. 


INTEREST 

DATES 

PER  CENTS 

INTERESTS  ON 

AMOUNTS  OF 

"• 

OF  INTEREST 

PRINCIPALS 

PRINCIPALS 

PRINCIPALS 

PAYMENTS 

Yr. 

Mo. 

Da. 

Yr. 

Mo. 

Da. 

1906 

1 

1 

1906 

3 

1 

2 

0 

$.01 

$1200.00 

$12.00 

$1212.00 

$212.00 

1906 

7 

1 

4 

0 

.02 

1000.00 

20.00 

15.00 

1906 

9 

1 

2 

0 

.01 

1000.00 

10.00 

1030.00 

515.00 

1906 

11 

1 

2 

0 

.01 

500.00 

5.00 

505.00 

175.00 

1907 

4 

1 

5 

0 

.025 

330.00 

8.25 

338.25 

1 

3 

0 

1 

3 

0 

$.075 

$338.25,  balance  due  Apr.  1,  1907 

334  PRACTICAL   BUSINESS   ARITHMETIC 

When  there  are  many  payments,  the  work  may  be  simplified  as  shown  in 
the  foregoing  outline.  First  write  the  date  and  the  face  of  the  note  and  then 
the  dates  and  the  amounts  of  the  payments.  Next  find  the  interest  periods 
and  the  per  cents  of  interest.  Test  the  accuracy  of  the  work  to  this  point 

(1)  by  finding  the  difference  between  the  date  of  the  note  and  the  date 
of  settlement  and  comparing  it  with  the  sum  of  the  interest  periods ;  and 

(2)  by  comparing  the  sum  of  the  per  cents  of  interest  with  the  interest  on  $1 
for  the  full  time  as  shown  by  the  sum  of  the  interest  periods.     Complete 
the  remainder  of  the  work  as  suggested  by  the  outline. 

WRITTEN  EXERCISE 

1.  Jan.   2,  1907,   J.    E.    King  &    Co.  borrowed   of   E.    B. 
Peterson  &  Bro.  $1000  and  gave  in  payment  a  note  payable  iij 
6  mo.,  with  interest  at  5%.     July  2,  J.  E.  King  &  Co.  made  a 
payment  of  $ 500  and  issued  a  new  note  at  90  da.,  with  interest 
at  6  %  for  the  balance  due.     What  was  the  face  of  the  new  note? 

2.  Jan.  30,  1906,  you  sold  Irwin  &  Co.  5  Eureka  Elevator 
Pumps  at  $475,  less  a  trade  discount  of  16-|%.     Terms:  note 
at  6  mo.  with  interest  at  6  % .     What  was  the  amount  of   the 
note  ?    At  the  maturity  of  the  note  Irwin  &  Co.  paid  you  cash 
$1000  and  gave  you  a  new  note  at  6  mo.,  with  interest  at  6% 
for  the  balance   due.     What  was  the  face  of  the  new  note? 
Sept.  1, 1906,  Irwin  &  Co.  paid  you  $200,  and  Dec.  1,  $300,  on 
their  note  of  July  30.      What  was  due  on  the  note  Feb.  9,  1907? 

3.  On  the  note  below  indorsements  were  made  as  follows: 
May  1,  1906,  $75;   Sept.   2,   1906,  $90;  Oct.   2,  1906,  $165; 
Jan.  2,  1907,  $125. 

$825.40  OMAHA,  NEB.,  Jan.  2,  1906. 

Apr.  2,  1907,  I  promise  to  pay  Wilson  &  Allen,  or  order, 
Eight  Hundred  Twenty-five  -^-fa  Dollars,  at  their  office,  with 
interest  at  6  %. 

Value  received.  JOHN  D.  AVERILL. 

What  was  due  at  the  maturity  of  the  note  ? 

4.  Find  the  amount  due  on  each  of  the  following  notes  July 
1,  1907  : 


PARTIAL    PAYMENTS 


335 


a. 


Rochester,  Jtf.., 


the  order 


<^^^  "/ 


^k^—  promise  to  pay  to 


Value  received 


I. 


t/ie  order  »f 


to  pay  to 


Value  received 
/£  9),,* 


•s  -s 


paytotke   order 


6/ 
date,  for  value  received- 


to 


Collar, 


-  ,  with  interest  at  the  rate  of^2^per  centum 
per  annum  during  the  said^^L^L&ZL^  and  for  such  further  time  as  the 
said  principal  sum  or  any  part  thereof  shall  remain  unpaid. 


336 


PRACTICAL   BUSINESS   ARITHMETIC 


*N     V 

N     CM 
X    X 


PARTIAL  PAYMENTS  337 

THE  MERCHANTS'  METHOD 

ORAL    EXERCISE 

1.  A  note  for  1500  is  dated  July  1,  1906,  payable  in  1  yr. 
with  interest  at  6%.     If  no  payments  have  been  made,  what  is 
due  on  the  note  July  1,  1907  ? 

2.  A  payment  of  $300  was  indorsed  on  the  note  Jan.  1,  1907. 
What  was  the  amount  of  this  payment  at  the  time  the  note  be- 
came due  ? 

3.  If  the  value  of  the  note  at  maturity  is  $530  and  the  value 
of  the  payment  $309,  what  is  the  balance  due  ? 

4.  By  the  United  States  method  what  is  the  balance  due  at 
maturity  on  the  note  described  in  problems  1  and  3  ?     How 
does  this  balance  compare  with  the  balance  in  problem  3  ? 

416.  The  merchants'  method  is  based  on  custom  rather  than 
on  legal  authority.     It  is  used  by  most  banks  and  business  men 
on  short-time  notes  and  other  obligations. 

The  principles  of  the  merchants'  method  are  suggested  in  problems  1-3. 
This  method  provides  that  :  (1)  the  face  of  the  note  shall  draw  interest  to  the 
date  of  settlement;  (2)  interest  shall  be  allowed  on  each  payment  from  the 
time  it  is  made  to  the  date  of  settlement. 

417.  Example.    On  a  note  for  $600,  dated  May  13,  1907,  pay- 
able on  demand,  with  interest  at  6%,  payments  were  made  as 
follows:  June  28,  1907,  $100;  Aug.  28, 1907,  $200.     What  was 
due  at  settlement,  Sept.  28,  1907? 

SOLUTION 

Face  of  note  May  13,  1907          . $600.00 

Interest  from  May  13,  1907,  to  Sept.  28,  1907  (4  mo.  15  da.)    .        .  13.50 

Value  of  note  Sept.  28,  1907,  the  date  of  settlement          .        .        .        $613.50 

Payment  June  28,  1907 $100.00 

Interest  on  this  payment  from  Aug.  28,  1907,  to  Sept.  28, 

1907  (3  ino.)        .         . 1.50 

Payment  Aug.  28,  1907 200.00 

Interest  on  this  payment  from  Aug.  28,  1907,  to  Sept.  28, 

1907  (1  mo.) 1.00 

Value  of  the  payments  Sept.  28,  1907,  the  date  of  settlement  .       $302.50 

Balance  due  Sept.  28,  1907,  the  date  of  settlement     ....        $311.00 


338 


PRACTICAL   BUSINESS   ARITHMETIC 


Some  houses  find  the  time  by  compound  subtraction  and  some  use  the 
exact  number  of  days.  In  the  following  exercise  find  the  difference  in  time 
by  compound  subtraction  in  problems  1-2,  and  use  the  exact  number  of  days 
in  problems  3-7. 

WRITTEN  EXERCISE 

1.  Solve  problem  a,  page  335,  by  the  merchants'  method  for 
partial  payments.     Compare  the  results  by  the  two  methods. 

2.  On  a  note  for  11200,  dated  Apr.  16,  1906,  payable  on  de- 
mand, with  interest  at  4|  %,  payments  were  made  as  follows: 
June  15,  1907,  1500;  July  18,  1907,  $200.     What  was  due  at 
settlement,  Sept.  16,  1907  ? 

3.  June  15  you  borrowed  $25,000  at  Traders'  National  Bank 
on  your  demand  note  secured  by  a  deposit  of  300  shares  of  New 
York,  New  Haven,  and  Hartford  Railroad  Stock  at  $170.     June 
27   you    paid  $5000,    July    2,   $10,000,  and  July  30,  $5000. 
Aug.  2  you  paid  the  remainder  of  the  note  and  interest,  and 
withdrew  the  collaterals.     What  was  the  amount  of  the  last 
payment,  money  being  loaned  at  4|  %  ? 

4.  The  following  is  a  partial  page  of  the  demand  and  loan 
register  of  a  large  bank.      Copy  it,  supplying  the  amount  of 
interest  due  Nov.  15,  money  being  loaned  at  4|  %. 

CHARLES  W.  SHERMAN 


No. 

DATE 
LOANED 

AMOUNT 
LOANED 

DATE  OF 
PAYMENT. 

PART  OF 
LOAN 
PAID 

BALANCE 
OF  LOAN 

INTER- 
EST 

COLLATERAL 

VALUE  on 
COLLAT- 
ERAL 

347 

Apr. 

1 

20,000 

00 

May 

15 

5,000 

00 

15,000 

00 

??? 

?? 

250  shares 

July 

1 

5,000  00 

10,00000;??? 

?? 

Penn.  R.R. 

Sept. 

1 

6,000  00 

4,000 

00??? 

?? 

Stock    .     . 

31,250 

00 

Nov. 

15 

4,000 

00 

1??? 

T? 

The  balance  due  by  the  merchants'  method  may  be  found  in  the  manner 
suggested  by  the  above  account.  The  interest  is  found  on  the  face  of  the 
note  to  the  date  of  the  first  payment.  The  payment  is  deducted  and  the  in- 
terest found  on  the  balance  to  the  date  of  the  second  payment,  and  so  on. 
The  results  obtained  by  this  process  are  exactly  the  same  as  the  results  ob- 
tained by  §  416. 


PARTIAL   PAYMENTS  339 

5.  Solve  problem  4  by  the  United  States  method  and  com- 
pare the  result  with  the  merchants'  method. 

6.  Assuming  that  the  collateral  note,  page  330,  has  the  fol- 
lowing payments  indorsed  on  its  back,  find  the  amount  due  at 
final  settlement,  Feb.  28,  1907.     Indorsements:    Jan.  15,  1907, 
13000  ;  Jan.  31,  1907,  15000  ;  Feb.  5,  1907,  $1000. 

7.  A  collateral  note  dated  at  Philadelphia,  Pa.,  July  10,  1907, 
for  $20,000  payable  at  the  Quaker  City  National  Bank  is  in- 
dorsed as  follows  :  Aug.  8,  1907,  $3500  ;  Sept.  12,  1907,  17500  ; 
Nov.  19,  1907,  14000  ;  Dec.  31,  1907,  $5000.     What  was  due 
on  the  note  Dec.  31,  1907,  interest  being  at  the  rate  of  4  %  ? 

To  solve  the  problem  copy  and  complete  the  following  interest  statement  : 


Philadelphia,  _  ^>T^    2-0  1  _  19 


To  THE  QUAKER  CITY  NATIONAL  BANK,  Dr. 

To  interest  on  demand  loans,  as  follows: 

$.,£./?/?  tftf-^  from  ?//0  tn  f/f  _  ,  2-&           fkys,  $  ? 

$/^  ^7/7-^  from  f/f  to  ?//2_  __cJ!^I_daysf  $  ? 

$    ^^7^7/7  —  from  ?//  2.  to  "//0  ?  ?             Jays,  $  ? 

^  frnm  ''/?  /  >n  '  '/?  ?  _        ?  .?             A*ys,  $  ? 


Please  send  us  the  above  interest  on  or  \*Stw* 


CASHIER 

8.  Make  an  interest  statement,  similar  to  the  above,  for 
problem  6. 

9.  Make  an  interest  statement,  similar   to   the  above,  for 
problem  3. 

10.  Bring  to  the  class  a  canceled  note  on  which  partial  pay- 
ments are  recorded.  Find,  by  the  United  States  method  and  by 
the  merchants'  method,  the  amount  required  to  cancel  the  note. 
Which  method  is  the  better  for  the  debtor?  for  the  creditor? 


CHAPTER   XXVIII 


BANKERS'   DAILY  BALANCES 

418.  Some  commercial  banks  and  trust  companies  pay  inter- 
est on  the  daily  balances  of  their  depositors. 

Whether  interest  shall  be  allowed  on  a  depositor's  account  is  usually 
determined  by  the  size  of  his  daily  balances.  As  a  rule,  no  interest  is 
allowed  on  small  balances  subject  to  check.  All  balances  not  subject  to 
check  usually  draw  interest.  In  an  active  account,  that  is,  an  account  in  which 
the  balance  changes  frequently,  interest  is  seldom  allowed  except  on  an  even 
number  of  hundred  dollars,  and  all  parts  of  a  hundred  dollars  are  rejected. 

The  form  of  the  book  in  which  accounts  with  depositors  are  recorded 
varies  in  different  sections.  What  is  known  as  the  Boston  individual  ledger 
(see  form,  page  38)  is  extensively  used.  Another  form  of  depositors'  ledger 
is  that  shown  in  the  example  below. 

419.  Example.     Verify  the   balance   due  on    the   following 
account  Mar.  1,  1907,  interest  settlements  being  made  monthly 
at  3%. 

M.    W.    P^ARNHAM 


EXPLANATION 

DATE 

F. 

DEBIT 

BALANCE 

CREDIT 

F. 

DATE 

Kxi'I.ANATION 

1907 

1907 

1056 

25 

Jan. 

1 

1656 

25 

600 

00 

15 

7 

Currency 

2556 

25 

900 

00 

15 

11 

N.  Y.  draft 

Check 

Jan. 

15 

14 

510 

00 

2046 

25 

3746 

25 

1700 

00 

17 

Jan. 

22 

N.  Y.  draft 

Note 

Jan. 

25 

16 

210 

00 

3536 

25 

Check 

28 

16 

500 

00 

3036 

25 

3042 

08 

5 

83 

17 

Jan. 

31 

Interest 

4042 

08 

1000 

00 

21 

Feb. 

8 

N.  Y.  draft 

Check 

Feb. 

15 

20 

500 

00 

3542 

08 

Check 

22 

22 

1340 

00 

2202 

08 

2209 

49 

7 

41 

23 

Feb. 

28 

Interest 

SOLUTION.  The  credit  slip  on  page  341  shows  a  form  used  for  recording  the 
daily  balances.  Only  two  money  columns  are  used,  one  for  hundreds  and  the 
other  for  thousands.  No  interest  is  computed  except  on  an  even  number  of 
hundred  dollars,  and  all  parts  of  a  hundred  dollars  are  rejected. 

340 


BANKERS'   DAILY   BALANCES 


341 


Beginning  with  Jan.  1  the  daily  balance  of  M.  W.  Farnkam's  account  for 
6  da.  was  $1056.25;  record  $1000  on  the  credit  slip  as  shown  in  the  margin. 
A  deposit  of  $600  was  made  Jan.  7,  making  the  balance  $1656.25  for  the  next 
4  da.;  record  $1600  on  the  credit  slip  as  shown  in  the  margin.  A  deposit  of 
$900  on  Jan.  11  made  the  balance  $2556.25 
for  the  next  4  da.;  record  $2500  on  the 
credit  slip  as  shown  in  the  margin.  A  with- 
drawal of  $  510  on  Jan.  15  left  a  balance  of 
$2046.25  for  the  next  7  da.;  record  $2000 
on  the  credit  slip  as  shown  in  the  margin. 
A  deposit  of  $1700  on  Jan.  22  made  the 
balance  $3746.25  for  the  next  3  da.;  record 
$3700  on  the  credit  slip  as  shown  in  the  mar- 
gin. A  withdrawal  of  $210  on  Jan.  25  left 
a  balance  of  $3536.25  for  the  next  3  da.; 
record  $3500  on  the  credit  slip.  A  with- 
drawal of  $500  on  Jan.  28  left  a  balance  of 
$3036.25  for  the  next  4  da.  This  records 
the  balance  for  each  day  in  January.  Add- 
ing these  balances  the  result  is  $70,000,  and 
the  interest  on  this  sum  for  1  da.  at  3%  is 
$  5. 83.  Adding  $  5. 83  to  $  3036. 25  gives  the 
balance  to  the  credit  of  the  depositor  Feb.  1 
as  $3042.08. 

Enter  the  daily  balances  for  February  as 
shown  in  the  margin.  The  result  is  found 
to  be  $88,900,  and  the  interest  on  this  sum 
for  1  da.  at  3%  is  $7.41.  $7.41  added  to 
the  balance  of  the  depositor's  account  Feb. 
28  gives  $  2209.41  as  the  balance  to  his  credit 
beginning  Mar.  1. 

In  practice  the  daily  balances  are  usually 
written  as  shown  in  the  February  column 
of  the  accompanying  credit  slip.  The  total 
is  then  found  by  multiplication  and  addi- 
tion. Thus,  the  total  of  the  February  col- 
umn is  7  x  $3000  +  7  x  $4000  +  7  x  $3500 


DAILY  CREDIT  BALANCES 

M.  W.  Farnham 

1907 

JAN. 

FEB. 

1 

1 

3 

2 

1 

3 

1 

4 

1 

5 

1 

6 

1 

7 

1 

6 

8 

1 

6 

4 

9 

1 

6 

10 

1 

6 

11 

2 

5 

12 

2 

5 

13 

2 

5 

14 

2 

5 

15 

2 

8 

5 

16 

2 

17 

2 

18 

2 

19 

2 

20 

2 

21 

2 

22 

3 

7 

2 

2 

23 

3 

7 

24 

3 

7 

25 

3 

5 

26 

3 

5 

27 

3 

5 

28 

3 

29 

3 

30 

3 

31 

3 

Total 

70 

~0~ 

88 

~9~ 

Interest 

5 

83 

7 

41 

+  7  x  §2200,  or  $88,900. 

Some  accountants  also  use  the  pure 
interest  method  in  finding  the  amount  due. 
Thus,  the  interest  on  $3000  for  7  da.,  plus  the  interest  on  $4000  for  7  da.,  plus 
the  interest  on  $3500  for  7  da.,  plus  the  interest  on  $2200  for  7  da.  equals  $7.41, 
the  same  as  by  the  first  method. 

In  the  examples  which  follow  the  student  may  use  either  of  the  three  methods 
suggested. 


342 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 

1.  The  Rochester  Trust  and  Safe  Deposit  Co.  allows  inter- 
est to  its  depositors  on  daily  balances  at  3  %  per  annum,  pay- 
able quarterly.     Find  the  cash  balance  of  the  following  account 
with  Chas.  M.  Sherman,  Apr.  1,  1907.     Jan.  1,  1907,  deposited 
$1200;    Jan.    12   drew  out  1400;    Jan.    30  deposited   $800: 
Jan.   31  drew  out  $400;    Feb.   10  deposited  $800;    Feb.   25 
drew  out  $100  ;   Mar.  10  deposited  $800  ;  Mar.   20  drew  out 
$900  ;  Mar.  25  deposited  $300. 

2.  Mar.  1,  1907,  Harvey  &  Smith's  balance  with  the  Fidelity 
Trust  Co.  was  $2246.     During  the  month  they  made  the  follow- 
ingdeposits:  Mar.  3,  $2500;   Mar.  9,  $1750;  Mar.  24, $2645.75; 
Mar.  28,  $  1310. 50  ;  Mar.  30,  $  500.    They  also  drew  out  by  check 
as   follows:  Mar.    4,  $1050;   Mar.  6,  $2000;  Mar.   8,' $720; 
Mar.  12,  $840.50  ;  Mar.  16,  $450  ;  Mar.   19,  $430  ;  Mar.  23, 
$1000  ;  Mar.  26,  $150  ;  Mar.  29,  $267.     How  much  interest 
should  be  credited  at  the  end  of  the  month,  the  rate  being  3  % 
per  annum  ?     What  was  the  balance  of  the   account  after  the 
interest  was  credited  ? 

3.  Find  the  cash  balance  of  the  following  account  May  31, 
1907,  assuming  that  interest  is  allowed  on  daily  balances  at  3  % 
and  added  to  the  account  monthly. 

A.  S.  OSBOBN 


EXPLANATION 

DATE 

F. 

DEBIT 

BALANCE 

CREDIT 

F. 

DATE 

EXPLANATION 

190T 

1907 

1200 

00 

1200 

00 

Mar. 

1 

N.  Y.  draft 

Check 

Mar. 

12 

100 

00 

1500 

00 

400 

00 

12 

Currency 

2000 

00 

500 

00 

25 

Currency 

Check 

31 

100 

00 

2400 

500 

00 

31 

N.  Y.  draft 

*#** 

*# 

* 

** 

31 

Interest 

**** 

** 

700 

00 

Apr. 

15 

N.  Y.  draft 

Note 

Apr. 

20 

50 

00 

**** 

** 

200 

00 

20 

N.  Y,  draft 

Check 

30 

1200 

00 

*#** 

*# 

* 

** 

30 

Interest 

#*** 

** 

250 

00 

May 

10 

Currency 

Check 

May 

31 

500 

00 

***# 

** 

# 

** 

31 

Interest 

CHAPTER   XXIX 

SAVINGS-BANK  ACCOUNTS 

420.  A  savings  bank  is  an  institution,  chartered  by  the  state, 
in  which  savings  or  earnings  are  deposited  and  put  to  interest. 

The  deposits  in  a  savings  bank  are  practically  payable  on  demand.  Most 
banks  reserve  the  right  to  require  notice  of  withdrawal  from  30  to  60  da. 
in  advance  ;  but  this  right  is  seldom  exercised. 

The  period  of  time  which  must  elapse  before  dividends  of  interest  are 
declared  is  called  the  interest  term.  Dividends  of  interest  are  usually  de- 
clared semiannually ;  but  in  some  sections  they  are  declared  quarterly.  The 
stated  days  on  which  balances  begin  to  draw  interest  are  called  interest  days. 
In  some  savings  banks  deposits  begin  to  draw  interest  from  the  first  of  each 
quarter ;  in  others,  from  the  first  of  each  month. 

In  nearly  all  savings  banks,  only  such  sums  as  have  been  on  deposit  for 
the  full  time  between  the  interest  days  draw  interest.  Thus,  if  the  interest 
days  begin  on  the  first  of  each  quarter,  only  those  sums  that  have  been  on 
deposit  for  the  full  quarter  draw  interest. 

421.  Interest   is  computed  on  an  even  number   of   dollars, 
and  all  fractions  of  a  dollar  are  rejected.     When  interest  is  not 
withdrawn  it  is  placed  to  the  credit  of  the  depositor  and  draws 
interest  the  same  as  any  regular  deposit.     Savings  banks  there- 
fore allow  compound  interest. 

422.  Examples.    1.    In  the    Wildey   Institution  for  Savings 
the  interest  term  is  6  mo.  and  the  interest  days  are  Jan.  1, 
Apr.  1,   July   1,  and  Oct.  1.     Verify  the  balance  due  on  the 
following  account  Jan.  1,  1907,  at  4%. 

SOLUTION.  The  account  was  opened  July  1,  1906,  by  a  deposit  of  $500. 
July  10  this  sum  was  increased  by  a  deposit  of  $10,  making  the  balance  $510; 
Aug.  14  this  sum  was  diminished  by  a  withdrawal  of  $  20,  making  the  balance 
$490;  Oct.  4  this  sum  was  diminished  by  a  withdrawal  of  $200,  making  the 
balance  $  290.  The  account  was  similarly  increased  and  diminished  until  Dec. 
31,  when  there  was  a  balance  of  $300.75  due  the  depositor. 

343 


344 


PRACTICAL   BUSINESS   ARITHMETIC 


i/ne     riitdey  Institution  for  Savings 


in  account  with 


DEPOSITS 


INTEREST 


PAYMENTS 


BALANCE 


2 


2-rt  0 


/  'ff 


3  £ 


3  / 


a  f 


The  smallest  balance  for  the  first  interest  period,  July  1  to  Oct.  1,  was  8490. 
The  interest  on  $490  for  3  mo.  at  4%  is  $4.90.  The  smallest  balance  for  the 
second  interest  period,  Oct.  1  to  Jan.  1,  was  .$290.  The  interest  on  8290  for 
3  mo.  at  4%  is  $2. 90.  $4.90  plus  $2.90  equals  $7.80,  the  dividend  of  interest 
due  the  depositor  Jan.  1.  Since  this  sum  is  not  withdrawn,  it  is  placed  to  the 
credit  of  the  depositor,  making  his  balance  $308.55. 

2.  In  the  Warren  Institution  for  Savings  interest  dividends 
are  declared  semiannually  and  the  interest  days  are  Jan.  1, 
Apr.  1,  July  1,  and  Oct.  1.  Verify  the  balance  due  on  the 
following  account  Jan.  1,  1907,  at  4%. 


barren  3fostttution  for 


in  account  toi 


DATE 


DEPOSITS  INTEREST  PAYMENTS  BALANCE 


,3  a  >o 


/  a 


/  0  S) 


- 


- 


SAVINGS-BANK   ACCOUNTS 


345 


SOLUTION.  The  smallest  balance  for  the  first  interest  period  was  $500  ;  the 
interest  on  $500  for  3  mo.  at  4%  is  $5.  The  smallest  balance  for  the  second 
interest  period  was  $800;  the  interest  on  $800  for  3  mo.  at  4%  is  $8. 
$  5  +  $8  =  $13,  the  total  interest  due  the  depositor  July  1.  $900  +  $  13  =  $  913. 
This  balance  remained  unchanged  for  the  next  6  mo.  The  interest  on  $913  for 
6  mo.  at  4  %  is  $  18.26.  $  913  +  $  18.26  =  $  931.26,  the  amount  due  the  depositor 
Jan.  1,  1907. 

WRITTEN   EXERCISE 

1.  Solve  example   1  above,  assuming  that  the  interest  days 
are  the  first  day  of  each  month  ;  also  example  2. 

2.  Copy    the    following    account,     supplying    the    missing 
amounts.     Interest  at  4J  %  ;  interest  days,  Jan.  1,  Apr.  1,  July  1, 
and  Oct.  1. 

MANHATTAN   SAVINGS   BANK 
IN  ACCOUNT  WITH  Mr.  Chas.  B.  Sherman 


DATE 

DEPOSTI 

s 

INTERES 

T 

PAY.  MEM 

s 

BALANCI 

l 

1906 

Jan. 
Jan. 

31 

oOO 

(JU 

100 

00 

#  *   # 

#  # 

Mar. 

1 

250 

00 

*  *  * 

*   * 

May 
May 
July 

6 
31 

1 

100 

00 

#    * 

*  * 

60 

00 

*  *.* 

*  *  * 
*  *  * 

*   * 
*   * 
*   * 

3.    Copy  and  complete  the  following  account.      Interest  at 
4%  ;  interest  days,  Jan.  1,  Apr.  1,  July  1,  and  Oct.  1. 

FIDELITY   SAVINGS   BANK 
IN  ACCOUNT  WITH  Mr.  Frank  M.  Ellery 


DATE 

DEPOSITS 

INTEREST 

PAYMENTS 

BALANCE 

1906 

Jan. 

1 

300 

00 

*  * 

*  * 

Mar. 

6 

200 

00 

#  # 

*  * 

Mar. 

30 

125 

00 

*  * 

* 

Apr. 

17 

165 

50 

*  * 

* 

July 

1 

100 

00 

*   # 

*    * 

*  * 

* 

Aug. 

15 

75 

00 

*  * 

* 

Aug. 

31 

58 

40 

#  * 

* 

Oct. 

1 

250 

00 

*  * 

* 

Dec. 

1 

110 

50 

*  * 

* 

1907 

. 

Jan. 

1 

*     #    j    #   #     1 

CHAPTER   XXX 


EXCHANGE 
DOMESTIC   EXCHANGE 

ORAL   EXERCISE 

1.  Mention   some    objections   to   sending  actual   money  by 
express. 

2.  If  §50  sent  by  mail  in  a  registered  letter  is  lost,  to  what 
extent  are  the  postal  authorities  liable? 

3.  In  what  ways  may  you  pay  a  debt  at  any   distant  point 
without  actually  sending  the  money  ? 

423.  The  process  of  settling  accounts  at  distant  points  with- 
out actually  sending  the  money  is  called  exchange. 

MONEY  ORDERS 

424.  Money  orders,  as  issued  by  post  offices,   express  com- 
panies, and   banks   are   frequently  used   in  making   payments 
at  a  distance. 

425.  A    postal  money  order  is  a  government  order  for  the 
payment  of  money,  issued  at  one  office  and  payable  at  another. 


UNITED  STATES  POSTAL  MONEY  ORDER. 


Boston  (Bad  Ba)  Station),  fa;    T-    84449 

JUl  26  1907 


346 


EXCHANGE 


347 


The  fees  (rate  of  exchange)  charged  for  postal  money  orders  are  : 
For  orders  for  sums  not  exceeding- 
Over  $30.00  to  $  40.00  15? 


$2.50 


3? 


Over  2.50  to  $  5.00  of 
Over  5.00  to  10.00  8? 
Over  10.00  to  20.00  10  ? 
Over  20.00  to  30.00  12? 


Over  40.00  to  50.00  18? 

Over  50.00  to  60.00  20? 

Over  60.00  to  75.00  25? 

Over  75.00  to  100.00  30? 


The  maximum  amount  for  which  a  single  postal  money  order  may  be 
issued  is  <$ 100.  When  a  larger  sum  is  to  be  sent,  additional  orders  must  be 
obtained.  When  an  order  is  issued,  the  money  is  riot  sent  from  one  post 
office  to  another.  The  transfer  is  merely  a  matter  of  bookkeeping,  the 
money  being  received  by  the  government  at  one  office  and  paid  out  at 
another.  If  a  postal  money  order  is  lost,  a  duplicate  may  be  obtained  from 
the  Post  Office  Department  at  Washington. 

426.  An  express  money  order  is  an  order  for  the  payment  of 
money,  issued  by  an  express  company  and  payable  at  any  of  its 
agencies. 


The  fees  charged  for  express  money  orders  are  the  same  as  those  for  postal 
money  orders.  The  maximum  amount  for  which  a  single  express  money 
order  may  be  issued  is  $50.  A  postal  money  order  must  not  bear  more 
than  one  indorsement ;  but  an  express  money  order  may  bear  any  number 
of  indorsements. 

427.  A  bank  money  order  (see  form,  page  348)  is  an  order 
for  the  payment  of  money  issued  by  a  bank  and  payable  at 
certain  other  banks  in  different  parts  of  the  country. 

The  charge  for  a  bank  money  order  is  usually  the  same  as  that  for  a  postal 
money  order. 


348 


PRACTICAL   BUSINESS   ARITHMETIC 


NOT  OVER 

FIFTY  DOLLARS     BOSTON   MAS 


428.  A  telegraphic  money  order  is  a  telegram  of  an  express 
or  telegraph  company,  at  any  given  place,  ordering  the  pay- 
ment of  money  at  another  designated  place. 

THE  UNION  TELE.GRAPH  CO. 

INCORPORATED 


23,000  OFFICES  IN  AMERICA 


CABLE  SERVICE  TO  ALL  THE  WORLD 


ROBERT  C.  CLOWRY,  President  and  General  Manager 


S  E  N  D  the  following  message  subject  to  the 
terms  on  back  hereof,  which  are  hereby  agreed  to. 

The  Union  Telegraph  Co. 


Boston,    Mass.,    July  27, 


19 


Rochester.  N.Y. 

Findable 

Charles 

Osgood 

ten          East         Avenue 

Fi  chant 

Findelkind 

The          Union 

Telegraph 

Co. 

These  telegrams  are  usually  in  cipher;  that  is,  in  a  language  not  under- 
stood by   those  who   are   unfamiliar  with    the    system   of    abbreviations 
(code)  used.     The  sender  and  the  receiver  must  each  have  a  code.     The 
following  code  will  illustrate  the  principle  of  telegraphing  in  cipher : 
CODE  WORD  MEANING 

Fichant  One  hundred  dollars 

Ficheron  One  thousand  dollars 

Findable  Please  pay of your  city  $— 

Findelkind  On  production  by  him  of  positive  evidence 

of  his  personal  identity. 

The  principle  of  a  telegraphic  money  order  is  the  same  as  that  of  a  postal 
money  order;  no  money  is  transferred  from  one  place  to  another.  The 
charge  for  an  order  is  usually  1%  of  the  amount  to  be  transmitted  plus 
twice  the  rate  for  a  single  ten-word  message. 


EXCHANGE  349 

The  following  are  the  rates  for  a  ten-word  message  from  Boston  to  the 
places  named  : 

New  York        $0.25  Chicago  $0.50  Galveston     $0.75 

Philadelphia     $0.25  San  Francisco    $1.00  Rochester    $0.35 

ORAL  EXERCISE 

1.  What  was   the   total   cost   to  the    sender  of   the   postal 
money  order,  page  346?   the  express  money  order,  page  347? 
the  telegraphic  money  order,  page  348?  the  bank  money  order, 
page  348  ? 

2.  What  will  be  the  total  cost  of  a  postal  money  order  for 
27f?  12.19?  15.28?  110.40?  $18.90?  145.10?  $35.89?  $125 
($100  +  $25)?  $75.29?  $49.82?  $127.16? 

3.  What  will  be  the  total  cost  of  an  express  money  order  for 
$6.20?  $28.80?  $19.50?  $27.95?  $48.90?  $65   ($50  +$15)? 
$111?  $37.59?  $41.72?  $65.59?  $114? 

4.  What  will  be  the  total  cost  of  a  telegraphic  money  order 
from  Boston  to  New  York  for  $50?  $75?  $100?  $125?  $150? 
$200?    $300?    $400?    $450?    $500?  from    Boston    to    Phila- 
delphia?   from   Boston    to    San    Francisco?    from    Boston   to 
Chicago  ? 

5.  Translate  the  following  telegraphic  money  order :  Find- 
able  F.  J.  Reed,  20  Park  St.  ficheron  findelkind.     How  much 
will  it  cost  for  such  an  order  from   Boston  to  Galveston?  from 
Boston  to  Chicago?  from  Rochester  to  Boston? 

WRITTEN  EXERCISE 

1.  Find  the  total  cost  of  5  postal  money  orders  for  the  fol- 
lowing amounts :  $3.10;  $8.19;  $25.06;  $18.50;  $20. 

2.  Find  the  total  cost  of  six  express  money  orders  for  the 
following  amounts :  $1.25;  $10;  $6.80;  $16.25;  $80;  $19.50. 

3.  Find  the  total  cost  of  the   following  telegraphic  money 
orders:    one  from  Boston   to  New    York   for  $50;   one  from 
Boston  to  Philadelphia  for  $500;    one  from    Boston   to    San 
Francisco  for  $175;  one  from  Boston  to  Galveston  for  $300; 
one  from  Boston  to  Rochester  for  $250. 


350 


PRACTICAL   BUSINESS   ARITHMETIC 


CHECKS  AND  BANK  DRAFTS 

429.  Business  men  usually  keep  their  money  on  deposit  with 
a  commercial  bank  or  trust  company  and  make  most  payments, 
at  home  and  at  a  distance,  by  check;  that  is,  an  order  on  a 
bank  from  one  of  its  depositors  for  the  payment  of  money. 


A  check  may  be  drawn  for  any  amount  so  long  as  it  does  not  exceed  the 
balance  on  deposit  to  the  credit  of  the  drawer.  It  may  be  drawn  payable 
to  :  (1)  the  order  of  a  designated  payee,  in  which  case  the  payee  must 
indorse  it  before  the  money  will  be  paid  over;  (2)  the  payee,  or  bearer,  in 
which  case  any  one  can  collect  it ;  (3)  "  Cash,"  in  which  case  any  one  can 

collect  it. 

C.B.  Sherman  &  Co.  and  E.  II. 
Robinson  &  Co.  in  the  foregoing 
check  both  reside  in  Boston.    On 
receiving  the  check,  E.  II.  Rob- 
inson &  Co.  indorse  it  and  de- 
posit  it   for    credit  with    their 
bank,  say  the  National  Shawmut 
Bank.    The  First  National  Bank 
and     the    National      Shawmut 
Bank,   as  well    as    each  of   the 
other    banks  in    the    city,     has 
many     depositors     who     draw 
INTERIOR  VIEW  OF  A  CLEARING  HOUSE.       checks  upon  it   which   are    de- 
posited by  the  payees  in  various  other  city  banks,  and  it  also  receives  daily 
for  credit  from  its  own  depositors  checks  drawn  upon  various  other  city 
banks. 

Each  bank  therefore  has  a  daily  balance  to  settle  or  to  be  settled  with 
each  of  the  other  banks.  To  some  it  has  payments  to  make  and  from 
others  it  has  payments  to  receive.  If  these  balances  were  adjusted  in 
money,  each  bank  would  have  to  send  a  messenger  to  each  of  the  debtor 


EXCHANGE  351 

banks  to  present  accounts  and  receive  balances.  This  would  be  a  risky 
and  laborious  task.  To  facilitate  the  daily  exchanges  of  items  and  settle- 
ments of  balances  resulting  from  such  exchanges  there  has  been  established 
in  every  large  city  a  central  agency,  called  a  clearing  house.  This  agency 
is  an  association  of  banks  which  pay  the  expense  of  conducting  it  in  pro- 
portion to  the  average  amount  of  their  clearings. 

Suppose,  for  example,  that  the  banks  constituting  a  clearing  house  are 
Nos.  1,  2,  3,  and  4.  No.  1  presents  at  the  clearing  house  items  against  Nos. 
2,  3,  and  4,  and  Nos.  2,  3,  and  4  present  items  against  No.  1.  So,  likewise, 
with  No.  2  and  each  of  the  other  banks.  In  the  clearing  house  there  are  usually 
two  longitudinal  columns  contain  ing  as  many  desks  as  there  are  banks  in  the 
association.  At  a  given  time  a  settling  clerk  from  each  bank  takes  his  place 
at  his  desk  inside  of  one  of  the  columns  and  a  delivery  clerk  from  each  bank 
takes  his  place  outside  the  column.  Each  delivery  clerk  advances,  one  desk 
at  a  time,  and  hands  over  to  each  settling  clerk  his  exchange  items  against  that 

bank.    After  the  circuit  of  the  desks  has         ^__ 

been  completed  each  delivery  clerk  is  at    OC 

the  point  from  which  he  started,  and  each 

settling  clerk  has  on  his  desk  the  claims  of 

all  of  the  other    banks  against  his  bank. 

Each   settling    clerk   then    compares    his 

claims  against  other  banks  with  those  of 

other    banks    against    him    and  strikes  a 

balance.     This  balance  may  be  in  favor 

of  or  against  the  clearing  house.     If  No.  1  brought  claims  against  Nos.  2,  3, 

and  4  aggregating  $211,000  and  Nos.  2,  3,  and  4  brought  claims  against 

No.  1  aggregating  $200,000,  there  is  $11,000  due  No.  1  from  the  clearing 

house.      But    if  No.  1  brought   to    the    clearing   house    exchange    items 

aggregating  $200,000  and  took  away  exchange  items  aggregating  $211,000, 

there   is    $11,000    due   the  clearing  house  from  No.  1.     So,  likewise,  with 

No.  2  and  each  of  the  other  banks.      When   all  of  the   exchanges   have 

been  completed,  the  clearing  house  will  have  paid  out  the  same  amount 

that  it  has  received. 

But  all  checks  received  by  banks  are  not  payable  in  the  city.  Suppose 
that  A.  W.  Palmer,  of  Chicago,  111.,  owes  C.  B.  Andrews,  of  Westfield, 
Mass.,  $500  and  that  the  amount  is  paid  by  a  check  on  the  City  National 
Bank  of  Chicago.  C.  B.  Andrews  receives  the  check  and  offers  it  for  credit  at 
the  Farmers  and  Traders  Bank  of  Westfield,  Mass.  The  Westfield  Bank  has 
no  account  with  any  Chicago  bank,  but  it  has  with  the  First  National  Bank 
of  Boston,  and  the  check  is  sent  to  that  bank  for  credit.  The  First  National 
Bank  wishes  to  increase  its  New  York  balance  and  the  check  is  forwarded 
to  Chemical  National  Bank  of  New  York  for  credit.  Chemical  National 
Bank  next  mails  the  check  to  Commercial  National  Bank  of  Chicago,  the 


352  PRACTICAL   BUSINESS   ARITHMETIC 

bank  with  which  it  has  regular  dealings  in  that  city.  Commercial 
National  Bank  sends  the  check  to  the  clearing  house  and  it  is  carried 
to  the  City  National  Bank  by  a  messenger  from  that  bank.  Thus,  all  of  a 
depositor's  checks  will  in  time  be  presented  to  the  bank  on  which  they  are 
drawn.  When  presented,  they  will  be  charged  to  the  depositor,  cancelled,  and 
later  returned  to  him  to  be  filed  as  receipts. 

Banks  frequently  charge  their  depositors  a  small  fee  (rate  of  exchange) 
for  collecting  out-of-town  checks.  This  fee  is  rarely  over  ^%,  but  there  is 
no  uniformity  in  the  matter.  Sometimes  when  a  customer  keeps  a  large 
bank  account,  no  charge  whatever  is  made  for  the  collection. 

430.  It  often  happens  that  a  person  will  find  it  necessary  to 
make  payment  to  one  who  does  not  care  to  take  the  risk  of  a 
private  check  or  to  one  who  should  not  be  called  upon  to  pay 
the  cost  of  cashing  a  check.  In  such  cases  some  other  form  of 
instrument  of  transfer  must  be  used.  A  very  common  and  con- 
venient method  of  making  a  remittance  is  by  means  of  a  check 
of  one  banking  institution  upon  another  called  a  bank  draft. 


^Boston, 

traders  ^National  djanK 

/- 

y  * 

^^ 

Jo   (3/iemical  ^National 
Jfeu, 


Banks  in  the  different  cities  frequently  keep  running  accounts  with  each 
other  and  make  periodical  settlements.  At  the  time  of  drawing  the  above 
draft  Traders  National  Bank  of  Boston  very  likely  has  checks  and  drafts 
drawn  upon  New  York  banks  which  it  has  received  from  its  depositors. 
These  it  sends  to  Chemical  National  Bank  to  cover  the  amount  of  the  draft. 
Corresponding  transactions  may  also  take  place  in  New  York.  Chemical 
National  Bank  may  sell  its  draft  on  Traders  National  Bank  and,  to  cover 
the  amount,  remit  checks  and  drafts  on  Boston  banks  which  it  has  received 
from  its  depositors.  What  is  occurring  between  these  two  places  is  also 
occurring  between  all  manner  of  places ;  but  drafts  upon  New  York  banks 
and  other  financial  centers  are  the  most  used  in  making  remittances. 


EXCHANGE  353 

A  bank  draft  is  sometimes  drawn  payable  to  the  one  to  whom  it  is  to  be 
sent.  It  is  better,  however,  to  have  it  drawn  payable  to  the  purchaser  who 
may  indorse  it  over  to  the  person  to  whom  it  is  to  be  sent.  In  this  way 
the  name  of  the  sender  appears  on  the  draft,  and  when  canceled,  the  draft 
will  serve  the  purpose  of  a  receipt.  Banks  usually  sell  drafts  at  a  slight 
premium  on  the  face.  This  premium  is  called  exchange.  It  varies  somewhat 
(see  page  358),  but  is  seldom  more  than  ^%. 

431.  There  are  still  other  methods  of  transmitting  funds 
through  the  instrumentality  of  a  bank.  A  depositor  may  ex- 
change his  own  check  for  that  of  a  cashier's  check.  The  latter, 
being  a  check  of  the  cashier  on  his  own  bank,  would  pass  among 
strangers  better  than  a  depositor's  check. 


Boston,  Mass.,       (^t^is  /?    19 

^r  f 

NATIONAL  SHAWMUT  BANK 
) 


the  order  of  (^^*z^^~*7  X/^^Z-^^—       $  2  *£*/<&  ^~ 


^ 


Dollars 


Cshier 


Iii  New  York  City  these  checks  are  occasionally  used  instead  of  the  New 
York  draft.  As  New  York  exchange  is  in  demand  in  all  parts  of  the 
country,  the  expediency  of  the  course  is  apparent. 

432.  By  depositing  a  sum  of  money  in  a  bank  a  person  may 
receive  a  certificate,  called  a  certificate  of  deposit.  This  will 
direct  the  payment  of  the  sum  deposited  to  any  person  whom 
the  depositor  may  name. 


on  the  return  of  this  certificate  properly  indorsed. 


The  payee  in  a  certificate  of  deposit  will  have  no  difficulty  in  getting  the 
certificate  cashed  or  the  amount  credited  to  him  by  his  bank. 


354  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL   EXERCISE 

1.  Assuming   that   the   bank    which   cashed    the    check   on 
page  5  charged  |  %  collection,  what  was  the  amount  credited 
to  the  depositor  ? 

2.  Silas  Long  of  New  York  deposited  the  following  check. 
The  bank  deducted  -^  %  for  collection.     How  much  was  placed 
to  Silas  Long's  credit? 


Union  33anfc 


3.  B  deposited  three  out-of-town  checks  in  his  bank  as  fol- 
lows :  $300;  |700;  1750.     If  the  bank  charged  -^%   collec- 
tion, what  amount  was  placed  to  B's  credit? 

4.  Bring  to  the  class  a  number  of  canceled  checks  and   take 
several  of  them  and  trace  them  from  the  time  they  were  issued 
until  they  were  filed  as  receipts  by  the  drawer.     Show  why  a 
canceled  check  is  the  best  kind  of  a  receipt  for  the  payment  of 
money  ? 

5.  How  much  did  the  bank  draft  on  page  352   cost  the  pur- 
chaser if  the  exchange  was  at  ^  %  premium  ? 


WRITTEN   EXERCISE 

1.  Find  the  cost  of  a  bank  draft  for  $3958.75  at  ^  %    pre- 
mium;  of  a  bank  draft  for  $679.80  at  ^%  premium;  of  a 
bank  draft  for  $768.54  at  50  J*  per  $1000  premium. 

2.  To  cover  the  cost  of  a  bank  draft  bought  at  -^%  pre- 
mium, I  gave  my  bank  a  check  for  $250.25.     What  was  the 
face  of  the  draft  ?      What  was  the  rate  of  premium  per  $1000? 


EXCHANGE 


355 


3.  Plow  large  a  bank  draft  can  be  bought  for  $850.85,  ex- 
change being  at  -fa  %  premium  ? 

4.  Find  the  proceeds  of  the  accompanying  deposit,  ^%  col- 
lection and  exchange  being  charged  on  the  out-of-town  checks. 


THE    UNION    NATIONAL    BANK 

DEPOSITED   BY 


Boston, 


L/L^< 


Specie 
Bills   ... 
Checks  .    . 


/2-ff 


g£ 


When  the  receiving  teller  takes  a 
deposit  from  a  customer,  he  classifies 
the  items  on  the  deposit  ticket,  as 
shown  in  the  accompanying  illustra- 
tion. If  the  coin  and  bills  passed  in 
count  right,  these  items  are  checked  (V) 
on  the  deposit  slip;  if  a  check  on  a 
clearing  house  bank  is  received,  it  is 
marked  with  the  number  of  that  bank 
in  the  clearing  house;  if  a  check  on 
the  teller's  bank  is  received,  it  is 
marked  "B";  if  a  check  on  an  out-of- 
town  bank  is  received,  it  is  marked 
"X." 

5.  Write  a  bank  draft  using 
the    following   data:    your   ad- 
dress and  the  current   date;  drawer,  Central  National  Bank; 
drawee,  Chemical  National  Bank,  New  York;  amount,  $711.94; 
payee,  C.  E.  Denison;  cashier,  your  name.     How  large  a  check 
will  pay  for  the  draft  at  ^ %  premium?     Write  the  draft. 

6.  Suppose  that  the  members  of  the  class  whose  surnames  be- 
gin with  the  letters  from  A  to  G  inclusive  have  a  deposit  with 
Traders   National   Bank  ;    that  the  members  whose  surnames 
begin  with  the  letters  from  H  to  N  inclusive  have  a  deposit 
with  City  National  Bank  ;   that  the  members  whose  surnames 
begin  with  O  to  S  inclusive  have  a  deposit  with  First  National 
Bank;  and  that  the  members  whose  surnames  begin  with  T  to  Z 
inclusive  have  a  deposit  with  Central  Bank.     Let  each  student 
write  a  check  on  his  bank  in  favor  of  one  of  his  classmates, 
and  let  this  classmate  indorse  the  check  and  deposit  it  with  his 
bank.     Then  form  a  clearing  house,  strike  a  balance  between 
the  different  banks,  and  have  these  balances  adjusted  by  the 
payment  of  school  money. 


356  PRACTICAL   BUSINESS   ARITHMETIC 


COMMERCIAL  DRAFTS 

433.    Business  men  frequently  employ  the  commercial  draft 
as  an  aid  in  the  collection  of  accounts  that  are  past  due. 


/  2.60.- 


bf. 

to  the  ort/er  of 


Value  received  and  charge  to  account  of 


The  above  is  a  common  form  of  draft  used  for  collection  purposes. 
Edgar  McMickle  owes  Wilbert,  Closs  &  Co.  $  260.50.  The  amount  is  due, 
and  Wilbert,  Closs  &  Co.  draw  a  draft  on  Edgar  McMickle  and  leave  it  with 
their  Springfield  bank  for  collection.  The  Springfield  bank  forwards  it  to 
its  correspondent  in  Paterson  and  this  bank  sends  it  by  messenger  to  Edgar 
McMickle.  When  he  pays  the  draft,  the  Paterson  bank  notifies  the  Spring- 
field bank,  and  that  bank  deducts  a  small  fee  (collection  and  exchange)  for 
collecting  the  draft,  and  credits  Wilbert,  Closs  &  Co.  for  the  proceeds. 

434.  It  has  been  seen  (page  321)  that  the  time  draft  is  fre- 
quently used  in  connection  with  sales  of  merchandise. 


t?          / 

^ ?Pay  to  the  order  of 


dollars 


Value  received  and  charge  to  account  of 


Jfo.^Z 


Suppose  Quincy,  Bradley  &  Co.  sell  L.  B.  Wade  &  Co.  a  bill  of  merchan- 
dise amounting  to  $500.  Terms:  30-da.  draft  for  the  amount  of  the  bill. 
The  draft,  as  above,  and  the  bill  in  regular  form  would  be  drawn  up  and 


EXCHANGE  357 

sent  to  L.  B.  Wade  &  Co.  for  acceptance.  The  object  of  drawing  a  time 
draft  in  connection  with  sales  of  merchandise  is  twofold :  (1)  when  ac- 
cepted, the  draft  serves  as  a  written  contract;  (2)  since  an  acceptance  is 
negotiable,  it  may  be  discounted  and  cash  realized  upon  it  before  maturity. 
Such  a  draft  is  frequently  left  with  a  bank  for  collection  instead  of  being 
remitted  with  the  bill.  The  bank  will  then  first  present  the  draft  for  accept- 
ance and  later  for  payment. 

ORAL   EXERCISE 

1.  If  you  exchange  your  check  for  a  cashier's  check,  is  there 
any  charge  for  the  accommodation  ? 

2.  If  the  sight  draft  on  page  356  was  collected  by  a  bank 
which   charged  \<J0   collection,  how  much  was  placed  to  the 
credit  of  Wilbert,  Gloss  &  Co.? 

3.  You  deposited  in  Shawmut  National  Bank  $5000,  received 
the  certificate  of  deposit  shown  on  page  353,  and  remitted  it 
to  E.  B.  Stanton  on  account.      Would  there  be  any  exchange  ? 

WRITTEN   EXERCISE 

1.  The  draft  on  page  356  was  accepted  July  17,  and  dis- 
counted  July   25.      If  the  bank  charged  -^  %  collection  and 
6  %  interest,  how  much  was  placed  to  the  credit  of  the  drawers  ? 

2.  Mar.   27  Wilson  Bros.,  Chicago,  111.,  drew  a  30-da.  draft 
on  E.  W.  King,  Toledo,  O.,  in  favor  of  themselves,  payable  30  da. 
after  date,  for  13500,  and  mailed  it  for  acceptance.     Apr.  1  the 
draft  was  received  accepted;   Apr.  2  it  was  discounted  at  City 
Bank.     If  the  charges  were  ^  %  collection  and  6  %  interest, 
what  amount  was  credited  to  Wilson  Bros.? 

3.  Apr.  17  O.  H.  Brooks,  Buffalo,  N.Y.,  drew  a  sight  draft 
on  Slocum  &  Co.,  Hartford,  Conn.,  in  favor  of  himself,  for  $391, 
and  left  it  with  his  bank  (First  National)  for  collection.     First 
National   Bank   sent  the    draft  to  its  Hartford  correspondent 
(Commercial  National),  and  5  da.  later  informed  O.  H.  Brooks 
that  the  draft  had  been  collected,  and  the  amount,  less  ^  %  col- 
lection, placed  to  his  credit.     If  O.  H.  Brooks's  bank  balance 
was  $ 758. 62  before  the  draft  was  drawn,  what  was  it  after  the 
draft  was  credited  ?    Write  the  draft  and  show  the  indorsements. 


358  PEACTICAL   BUSINESS   ARITHMETIC 

4.  Aug.  9  you  sold  C.  D.  Mead  &  Co.,  San  Francisco,  Cal., 
39  mahogany  sideboards  at  $  162. 50,  delivered  the  goods  to  the 
Interstate  Transportation  Co.,  and  received  a  through  bill  of 
lading  (receipt  for  the  goods  and  an  agreement  to  transport 
and  deliver  them  to  the  consignee  or  to  his  order).  You  then 
drew  a  sight  draft  on  C.  D.  Mead  &  Co.  in  favor  of  your  bank, 
attached  the  draft  to  the  bill  of  lading,  and  left  it  with  your 
bank  for  collection.  Your  bank  indorsed  the  draft  and  the  bill 
of  lading  and  sent  them  to  First  National  Bank  of  San  Fran- 
cisco for  collection  and  credit.  Aug.  23  you  received  advice 
that  the  draft  had  been  collected,  and  the  amount,  less  |  %, 
placed  to  your  credit.  What  was  the  amount  credited  ? 

When  First  National  Bank  of  San  Francisco  received  the  draft,  it  notified 
C.  D.  Mead  &  Co.  They  paid  the  draft,  and  the  bank  gave  them  the  bill  of 
lading.  When  goods  are  shipped  in  this  manner,  the  transportation  company 
will  not  deliver  the  goods  until  the  consignee  presents  the  bill  of  lading. 

FLUCTUATION  OF  RATES  OF  EXCHANGE 

435.  It  has  been  seen  that  money  orders  always  sell  for  more 
than  their  face  value,  and  that  bank  drafts  frequently  cost  a 
little  more  than  their  face  value.  When  exchange  costs  its 
face  value,  it  is  said  to  be  at  par :  when  it  costs  more  than  its 
face  value,  it  is  said  to  be  at  a  premium ;  when  it  costs  less  than 
its  face  value,  it  is  said  to  be  at  a  discount. 

On  bank  drafts  for  small  sums,  say  $  500  or  less,  exchange  is  usually  at 
a  uniform  premium.  This  premium  is  to  pay  the  banks  for  their  trouble 
and  the  expense  of  shipping  money  to  the  centers  on  which  the  drafts  are 
drawn,  when  balances  at  these  points  become  low.  But  exchange  on  the 
trade  centers  of  the  country  may  be  at  par  at  one  time,  at  a  premium  at 
another,  and  at  a  discount  at  still  another.  For  example,  during  the  late 
fall  months,  when  the  grain  crops  begin  to  be  sent  East,  New  York  is  send- 
ing a  great  many  checks  and  drafts  to  the  section  of  which  Chicago  is  the 
trade  center.  Exchange  on  New  York  is  then  very  plentiful  in  Chicago,  and 
if  a  man  in  Chicago  wished  to  buy  a  draft  on  New  York  for  a  large  amount, 
say  $10,000  or  more,  the  Chicago  banks  will  sell  it  to  him  at  a  discount. 
But  if  a  man  in  New  York  at  that  time  wished  to  buy  a  draft  on  Chicago 
for  $10,000,  he  would  have  to  pay  a  premium,  because  the  New  York 
banks  would  be  anxious  not  to  decrease  their  Chicago  balances. 


EXCHANGE  359 

Early  in  the  spring,  when  New  York  importers  and  jobbers  are  sending 
foreign  and  domestic  manufactured  goods  for  distribution  in  the  West,  a 
great  many  checks  and  drafts  are  being  sent  from  the  West  to  New  York,  and 
exchange  is  at  a  discount  in  New  York  and  at  a  premium  in  Chicago.  This 
principle  applies  at  any  trade  centers  between  which  exchange  operations  go 
on.  Smaller  places  make  their  settlements  in  or  through  larger  places,  and 
the  main  exchange  transactions  go  on  between  the  few  leading  cities,  with 
converging  lines  on  New  York. 

The  rate  of  exchange  between  two  cities  will  never  exceed  the  cost  of 
shipping  actual  money  from  one  of  the  cities  to  the  other,  except  in  time  of 
panic  or  a  financial  unrest.  Thus  when  the  cost  of  sending  money  by  express 
from  New  York  to  Chicago  is  $5  per  $  10,000,  the  discount  in  New  York  or 
the  premium  in  Chicago  will  not  greatly  exceed  £Q%  ($5  per  $  10,000). 
To  prevent  the  rates  from  going  any  higher  the  banks  will  arrange  for  the 
shipment  of  actual  money  from  New  York  to  Chicago. 

As  a  rule  no  charge  is  made  for  cashing  bank  drafts  on  the  trade  centers 
of  the  country,  like  New  Yrork,  Chicago,  and  Philadelphia. 

436.  It  has  been  seen  that  banks  frequently  charge  a  small 
fee  for  collecting  paper  payable  out  of  town. 

In  some  cases  the  rates  of  collection  are  more  or  less  arbitrary ;  in  others 
they  are  governed  by  trade  movements,  the  same  as  rates  of  exchange.  Jn 
still  others  the  clearing  house  association  fixes  the  rate. 

ORAL   EXERCISE 

Find  the  cost  of  the  following  bank  drafts: 

1.  $18,500  at  gV  %  discount ;  at  40  j*  per  1 1000  premium. 

2.  $ 516.90  at  -^  %  premium  ;  at  50  £  per  $  1000  discount. 

3.  $1600.80  at  75^  per  $1000  premium  ;  at  T^  %  discount. 

4.  A    draft  for  $4000  was    bought   for   $3998.     Was   ex- 
change at  a  premium  or  at  a  discount,  and  what  rate? 

5.  J.  E.  Smith  &  Co.   drew  at  sight  on  E.  M.  Barrows  for 
$250  and  made  collection  through  their  bank.     If  the  bank 
charged  -£$%  for  collection,  for  what  amount  did  J.  E.  Smith 
&  Co.  receive  credit  ? 

6.  During  the  late  fall  many  checks  and  drafts  are  being 
sent  to  the  southern  cities  in  payment  for  shipments  of  cotton. 
At  such  times  is  exchange  on  New  York  likely  to  be  at  a  dis- 
count or  at  a  premium  in  New  Orleans  ?  in  New  York  ? 


360  PRACTICAL   BUSINESS    ARITHMETIC 

7.  Frank  M.  Burton  wishes  to  collect  an  account  oi  §70.58 
and  for  this  purpose  draws  the  following  draft  and  leaves  it 
with  the  National  Express  Co.  for  collection.  If  the  express 
company  charges  25^  for  collection,  how  much  will  it  collect 
of  Fred  W.  Greenlaw  ?  how  much  will  it  pay  Frank  W. 
Burton  ? 


_Pay  to  the 

' 


order  of_ 


.Dollars 


Value  received  and  charge  the  same  to  account  of 

With  current  rate  of  Exchange 


To_ 

Wo. Jfe*^^Z^L^X  2fo0r         \ 

Note  that  the  draft  contains  the  clause  "  With  current  rate  of  Exchange." 
This  means  that  the  drawee  is  requested  to  pay  the  face  of  the  draft  plus 
the  cost  of  exchange.  Nearly  all  express  companies  have  arrangements  by 
which  they  undertake  the  collection  of  notes  and  accounts.  The  process  of 
collecting  is  simple.  The  note  or  draft  covering  the  amount  of  the  account 
is  placed  in  a  collection  envelope  furnished  by  the  express  company,  and  sent 
to  its  destination.  Tf  collection  cannot  be  made,  notice  is  given  with  reasons 
for  refusal ;  if  collection  is  made,  the  money  is  sent  back  in  the  collection 
envelope,  and  the  amount,  less  collection  charges,  paid  to  the  one  for  whom 
the  collection  was  undertaken.  The  charge  varies  with  the  distance. 

WRITTEN  EXERCISE 

1.  A   bank   draft   for   $15,000  was  bought  for  $14,992.50. 
Was  exchange  at  a  premium  or  at  a  discount,  and  what  rate  ? 
At  this  rate  find  the  cost  of  a  draft  for  $17,121.98  ;    a  draft  for 
$12,929.75  ;  a  draft  for  $127,162.89. 

2.  I  gave  the  American  Express  Co.  an  account  of  $178.50 
for  collection.     If  the  collection  charges  were  $  2.50  per  $1000, 
how  much  did  I  receive  from  the  company?     At  this  rate  what 
should  be  the  proceeds  from  the  collection  of  three  drafts  with 
amounts  as  follows  :  $125.60  ;  $218.90  ;  and  $134.50  ? 


EXCHANGE 


361 


3.  An  agent   sold  for  me  1000  T.  hay  at  117.50  per  ton. 
He  paid  $125  for  cartage,  175  for  storage,  charged  2J^>  com- 
mission, and  remitted  the  proceeds  by  a  bank  draft  bought  at 
\<fo  premium.     What  was  the  face  of  the  draft? 

4.  A  Boston  commission  merchant  sold  for  his  principal  in 
Chicago  27,518  Ib.  leather  at  25|^  per  pound.     If  he  charged  a 
commission  of  4^%,  how  large  a  bank  draft,  bought  at  $  1.50 
per  flOOO  premium,  should  he  remit  to  his  principal? 

5.  Mar.   8   Edward  Whitman  &  Co.   drew  a  draft  payable 
30  da.  after  date  on  El  wood  &  Spears  for  §375.98  and  had  it 
discounted  at  City  Bank.       If  the  rate  of  collection  was  ^  % 
and  interest  5%,  what  were  the  proceeds  of  the  draft? 

6.  Copy    and    complete    the    following    letter    of    advice, 
assuming  that  the  rate  of  collection  is  \%  on  Nos.   720  and 
716,  and  -fa  %  on  Nos.  692  and  710.     Check  the  results. 


NATIONAL  EXCHANGE  BANK 

ALBANY,  N.Y.,        &&(>-.  12,        19 

MR.      &ka&.  1-i}-.   f'fa'm.Lttom,,      Cashier 
7HcA^wunt^>  cAat>i;&n>a,t  Mdnfa 

DEAR  SIR,  —  We  credit  your  account  this  day  for  the  proceeds  of 
collections  as  stated  below.                        Respectfully  yours, 
L.    H.    PIERSON,   Cashier 

YOUR  NO. 

PAYER 

AMOUNT 

CHARGES 

PROCEEDS 

720 

€.  e,.  initu 

soo 

00 

/ 

00 

799 

00 

Yt6 

10.  €.  &wf 

qoo 

75 

* 

** 

*** 

** 

6<?g 

(H.  <&.   /Send  ty  (&&. 

3750 

50 

* 

** 

**** 

** 

7/0 

1&.  &.  Lo-ny  ty  £/!wi 

37500 

00 

** 

** 

***** 

** 

?*lb/ 

25 

** 

** 

***** 

** 

362  PRACTICAL   BUSINESS   ARITHMETIC 

FOREIGN  EXCHANGE 

FOREIGN  MONEY 

ORAL  EXERCISE 

1.  Repeat  the  table  for    English   money.     (See  Appendix 
page  441)  ;  for  French  money  ;    for  German  money. 

2.  What  is  the  value  of  a  pound  sterling  in  United  States 
money  ?  of  a  franc  ?  of  a  mark? 

3.  Express  $4866.50  in  English  money;    £100  in   United 
States  money.     Express  $  1930  in  French  money  ;  1000  fr.  in 
United    States    money.       Express    $  238    in  German  money; 
10000  M.   in  United  States  money. 

A  pound  sterling  is  commonly  thought  of  as  about  $5;  a  shilling  or  a 
mark  as  about  25  ^ ;  a  penny  as  about  2  ^ ;  a  franc  or  lira  as  about  20  ^ ;  a 
guilder  as  about  40  J*.  In  problems  4-6  use  these  approximations. 

4.  Express   1100  as    English    money  ;  as    German    money  ; 
as  French  money;  1500  guilders  in  United  States  money. 

5.  Express  as  United  States  money:   £15;    £  8  5s.  ;    £25 
10s.;    100  M.;   1500  M.  ;   1750  M.  ;   75  fr.  ;   350  fr.;   200  fr. 

6.  A  and  B  while  abroad  spent  3  wk.  in  Naples,  Italy.     If 
their  expenses  here  averaged  25  lire  apiece  per  day,  how  much 
was  this  in  United  States  money  for  the  3  wk.  ? 

WRITTEN  EXERCISE 

1.  Express  as  pounds  and  decimals  of  a  pound  :    £25  6s.  ; 
£150  15s. ;   £200  10s.  6d.;  £300  12s.  M. 

2.  Reduce  to  United  States  money  :  £25  10s. ;  £120  9s. 

3.  Reduce  to  United  States  money:  275  M.;  1500  M.  75  pf. ; 
315  fr.;  725    fr.;    £115    10s.    Qd.     Reduce   $1250  to   English 
money  ;  to  French  money  ;  to  German  money. 

4.  In  a  recent  year  the  funded  debt  of  the  German  Empire 
amounted  to  2,733,500,000  M.,  of  which  1,240,000,000  M.  bore 
interest  at   3|%    and   1,493,500,000  M.    at   3%.      Express   in 
United  States  money  the  interest  on  the  funded  debt  for  1  yr. 


EXCHANGE  363 

THE  METRIC  SYSTEM 

437.  The  metric  system  is  a  system  of  measures  having  a 
decimal  scale  of  relation.  It  was  invented  by  France,  and  is 
now  used  in  practical  business  in  a  large  part  of  the  civilized 
world.  It  has  been  authorized  by  law  in  Great  Britain  and 
the  United  States,  but  is  not  generally  used  in  these  countries 
except  in  foreign  trade  and  in  scientific  investigations. 

The  principal  units  of  the  system  are  the  meter  for  length,  the  liter  for 
capacity,  and  the  gram  for  weight.  Stibmultiples  and  multiples  of  these 
units  are  easily  learned  when  the  meaning  of  the  prefixes  is  known.  The 
Latin  prefixes,  deci,  centi,  and  milli  mean  respectively  0.1,  0.01,  and  0.001  of 
the  unit.  The  Greek  prefixes  deca,  hekto,  kilo,  and  myria  mean  respectively, 
10,  100,  1000,  and  10,000  times  the  unit. 

TABLE  OF  LENGTH 

10  millimeters  (mm.)  =  1  centimeter  (cm.)        —  .01  meter. 

10  centimeters  =  1  decimeter  (dm.)        =  .1  meter. 

10  decimeters  =  1  meter  (m.)  1.  meter. 

10  meters  =  1  dekameter  (Dm.)      =         10.  meters. 

10  dekameters  =  1  hektometer    (Hm.)  =       100.  meters. 

10  hektometers  =  1  kilometer  (Km.)  1000.  meters. 

10  kilometers  =  1  myriameter  (Mm.)  =  10,000.  meters. 

The  units  in  common  use  are  indicated  by  black-faced  type. 
TABLE  OF  SQUARE  MEASURE 

100  sq.  millimeters  =1  sq.  centimeter  (sq.  cm.)  .001  sq.  meter. 

100  sq.  centimeters  =1  sq.  decimeter  (sq.  dm.)  .01  sq.  meter. 

100  sq.  decimeters    =1  sq.  meter  (sq.  m.)  1.    sq.  meter  =  1  centare. 

100  sq.  meters  =1  sq.  dekameter  (sq.  Dm.)  =  100.    sq.  meters  =  1  are. 

100  sq.  dekameters  =1  sq.  hektometer  (sq.  Hm.)=          10,000.    sq.  meters  =1  hectare. 

100  sq.  hektometers  =  lsq.  kilometer  (sq.  Km.)  1,000,000.    sq.  meters. 

100  sq.  kilometers    =1  sq.  myriameter  (sq.  Mm.)  =100,000,000.    sq.  meters. 

The  centare,  are  (a.),  and  hektare  are  common  terms  in  land  measure- 
ments. 

TABLE  OF  CUBIC  MEASURE 

1000 cu.  millimeters     :=  cu.  centimeter  (cu.  cm.)  .000001  cu.  m. 

1000  cu.  centimeters    =  1  cu.  decimeter  (cu.  dm.)  .001        cu.  m. 

1000  cu.  decimeters      =  1  cu.  meter  (cu.  m.)  1.  cu.  m. 

1000  cu.  meters  =  1  cu-  dekameter  (cu.  Dm.)    =  1000.  cu.  m. 

1000  cu.  dekameters     ==  1  on.  hektometer  (cu.  Hm.)  =  1,000,000.  cu.  m. 

1000  cu.  hektometers  =  1  cu.  kilometer  (cu.  Km.)  1,000,000,000.  cu.  m. 

1000  cu.  kilometers      =  1  cu.  myriameter  (cu.  Mm.)  =  1,000,000,000,000.  cu.  m. 

The  cubic  meter  is  also  called  a  stere,  a  unit  used  in  measuring  wood. 


364 


PKACTICAL   BUSINESS   ARITHMETIC 


10  inilliliters  (ml.) 
10  centiliters 
10  deciliters 
10  liters 
10  dekaliters 
10  hektoliters 


TABLE  OF  CAPACITY 
=  1  centiliter  (cl.) 
=  1  deciliter  (dt.) 
=  1  liter  (1.) 
=  1  dekaliter  (Dl.) 
=  1  hektoliter  (HI.) 
=  1  kiloliter  (Kl.) 


A  liter  is  the  same  as  a  cubic  decimeter. 

TABLE  OF  WEIGHT 
10  milligrams  (mg.)  =  1  centigram  (eg.) 


10  centigrams 
10  decigrams 
10  grams 
10  dekagrams 
10  hektograms 
10  kilograms 
10  myriagrams 
10  quintals 


=  1  decigram  (dg.) 
=  1  gram  (g.) 
=  1  dekagram  (Dg.) 
=  1  hektogram  (Hg.) 
=  1  kilogram  (Kg.) 
=  1  myriagram  (Mg.) 
=  1  quintal  (Q.) 
=  1  tonneau  (T.) 


The  tonneau  is  usually  called  a  metric  ton. 


=          .01  liter. 
.1    liter. 
=        1.      liter. 
=      10.      liters. 
=    100.      liters. 
=  1000.      liters. 


.01  gram. 


1 

gram. 

1. 

gram. 

10. 

grams. 

100. 

grams. 

1000. 

grams. 

=      10,000. 

grams. 

=    100,000. 

grams. 

=  1,000,000. 

grams. 

TABLE  OF  APPROXIMATE  VALUES 


A  meter 
A  kilometer 
A  square  meter 
An  are 
An  hectare 
A  cubic  meter 


=  3Jft.  or  1.1  yd. 

=  f  mi. 

=  1^  sq.  rd. 

=  4  sq.  rd. 

=  2JA. 

=  1.3  cu.  yd. 


A  stere  =  T3r  cd. 

A  gram  =  15^  gr. 

A  kilogram      =  21  lb.  av. 
A  liter  =  1  qt. 

An  hektoliter  =  2£  bu. 
A  meti-ic  ton    =  2200  lb. 


ORAL  EXERCISE 

1.  Name  the  prefix  which  means  10,000  ;  0.001 ;    100 ;   0.01 ; 
10;  0.1;  1000. 

2.  Read     the     following:      2.5m.;      72  mm.;      95.5  cm.; 
302.05    km.     Express    475.125    m.    in   millimeters  ;    in   hek- 
tometers. 

3.  Which    of     the   divisions    of    the   following    scale    are 
millimeters?  centimeters? 


0             , 

!     2 

y 

4 

5 

6 

7 

8 

y 

10 

imiini 

1 

1  decimeter 


EXCHANGE  365 

4.  A  certain  tower  is  200  m.  high;  this  is  approximately 
how  many  feet? 

5.  How  many  square  meters  in  1  a.  ?   how  many  ares  in 
5  Ha.  ?  in  25  Ha.  ? 

6.  How  many  liters  in  1  cu.  m.?   in  5  cu.  m.?     Find  the 
cost  of  5  Kl.  of  milk  at  5^  a  liter  ;  at  4^  a  liter. 

7.  Find   the    length    of    your   schoolroom   in  meters;    the 
weight  of  any  familiar  object  in  kilograms. 

8.  Bought  1000  m.  of  cloth.      How  many  yards  was  this  ? 

9.  An  importer  bought  1000  1.  of  liquors  at  80^  a  liter.     If 
he  sold  it  at  $  3.50  per  gallon,  did  he  gain  or  lose,  and  how  much  ? 

10.    The  distance  from  Paris  to  Cologne  is  510  Km.;   from 
Cologne  to  Mainz  150  Km.     Express  these  distances  in  miles. 

WRITTEN  EXERCISE 

1.  At  $75  an  acre  find  the  cost  of  75  Ha.  of  land. 

2.  Find  the  cost  of  175.75  m.  of  lace  at  65^  a  meter. 

3.  How  many  steres  of  wood  in  a  pile  12  m.  long,  1.5  m. 
wide,  and  3  m.  high?     How  many  cords? 

4.  A  merchant  bought  cloth  at  11.14  per  meter,  including 
duties.     For  how  much  must  he  sell  it  per  yard  to  gain  33|%? 

5.  I  imported  1000  m.  of  silk  (see  duties,  page  288)  at  10  fr. 
per  meter  and  sold  it  at  §3  per  yard.     Did  I  gain  or  lose  and 
how  much,  the  silk  being  1  yd.  wide? 

6.  The  distance  between  two  places  on  a  map  is  15.5  cm. ; 
this  is  10-^00  of  the  actual  distance.     What  is  the  actual  dis- 
tance in  miles? 

7.  C  bought  cloth  at  f>  2  per  meter,  including  duties,  and 
sold  it  by  the  yard  at  a  gain  of  25%.     What  was  the  selling 
price  per  yard? 

8.  The  speed  rate  of  a  certain  express  train  is  64  Km.  an 
hour ;  of  a  certain  mail  train,  48  Km.  an  hour.     In  a  journey  of 
384  Km.  what  time  will  be  saved  by  taking  the  express  instead 
of  the  mail  train. 


366  PRACTICAL   BUSINESS   ARITHMETIC 

FOREIGN  MONEY  ORDERS 

438.  Small  sums  are  frequently  sent  from  one  country  to 
another  by  means  of  foreign  money  orders. 

The  international  postal  money  order  and  the  foreign  express  money  order 
or  check  are  both  extensively  used  for  this  purpose.  These  orders  are 
usually  drawn  payable  in  the  money  of  the  country  on  which  they  are  issued. 
They  are  similar  in  form  to  domestic  money  orders,  but  are  issued  on  prac- 
tically the  same  principle  as  the  ordinary  bank  draft. 

ORAL   EXERCISE 

1.  D  in  Chicago  wishes  to  send  E  in  Havre,  France,  780  fr. 
At  19.5^  to  the  franc,  how  large  an  express   money  order  (in 
francs)  can  he  buy  ? 

2.  B  in   New  York   wishes  to  send  $120  to  C  in  Leipzig, 
Germany.     At  24^  to  the  mark,  how  large  an  express  money 
order  (in  marks)  can  he  buy  ? 

3.  At  \°/o  premium   find  the  cost  of  an  international  money 
order,  payable  in    Great    Britain,    for   each  of   the    following 
amounts:  $40;  $50;   175;  $100;  $150;  $200. 

4.  A   in  Boston  bought   an   international    money  order  for 
$20  and  sent  it  to  a    friend  in    Liverpool,  England.     At  1% 
premium,    what  did  the  order  cost?     For  how  many    pounds 
sterling  (approximately)  was  it  issued  ? 

WRITTEN   EXERCISE 

1.  I  wish  to  send  $100  to  G  in   Holland.      At  40|  ^  to  the 
guilder,  how  large  an  express  money  order  can  I  buy  ? 

2.  I  wish  to  send  $50  to  a  friend  in  Scotland.     At  $4.87  to 
the  pound,  how  large  an  express  money  order  can  I  buy  ? 

3.  C  in  Chicago  sent  D  in  Geneva  an  express  money  order 
for  256.41  fr.     At  19.5^  to  the  franc,  how  much  did  the  order 
cost  C  ? 

4.  E  in  Philadelphia  sent  F  in  Naples  an  international  postal 
money  order  for  128.21  lira.     At  19.5^  to  the  lira,  how  much 
did  the  order  cost  E  ? 


EXCHANGE 


367 


BILLS  OF  EXCHANGE 

439.   Drafts  of  a  person  or  a  bank  in  one  country  on  a  person 
or  a  bank  in  another  country  are  usually  called  bills  of  exchange. 


? 


94.3K1 


-•//,  JU1   10  1906 


MESS1??  liKOTOT,  SUIPLKY  A  CO. 


a 


440.  Bills  of  exchange  may  be  divided  into  three  classes: 
(1)  bankers'  bills,  which  are  drawn  by  one  banker  upon  an- 
other ;    (2)    commercial  bills,  which  are  drawn  by  one   mer- 
chant upon  another ;   (3)  documentary  bills,  which  are  drawn 
by  one  merchant  upon  another  and  secured  by  the  assignment 
and  transfer  of  a  bill  of  lading  and  policy  of  insurance  covering 
merchandise  on  its  way  to  the  market. 

The  foregoing  form  is  a  bankers'  demand  draft  or  check. 

Bankers'  bills  of  exchange  are  frequently  issued  in  duplicate ;  that  is,  in 
sets  of  two  of  like  tenor  and  amount.  These  bills  are  sometimes  sent  by 
different  mails;  but  more  frequently  the  original  is  sent  and  the  duplicate 
is  placed  on  file  to  be  sent  in  case  of  necessity.  Duplicate  bills  are  so  con- 
ditioned that  the  payment  of  one  of  them  cancels  the  other.  The  bankers' 
sole  bill  of  exchange  is  also  used.  This  is  preferred  by  many,  inasmuch  as 
it  may  be  more  easily  negotiated  by  the  payee  when  he  resides  in  a  city  other 
than  the  one  drawn  upon.  Commercial  and  documentary  bills  of  exchange 
are  usually  issued  in  duplicate. 

441.  The  mint  par  of   exchange  is  the  actual    value  of   the 
pure  metal  in  the  monetary  unit  of  one  country  expressed  in 
terms  of  another. 


368  PRACTICAL   BUSINESS   ARITHMETIC 

The  mint  par  of  exchange  is  determined  by  dividing  the  weight  of  pure 
gold  in  the  monetary  unit  of  one  country  by  the  weight  of  pure  gold  in  the 
monetary  unit  of  another.  Thus,  the  United  States  gold  dollar  contains 
23.22  troy  grains  of  pure  gold  and  the  English  pound  sterling,  113.0016  troy 
grains.  113.0016  +-23.22  =  4.8665.  Since  there  is  4.8665  times  as  much  pure 
gold  in  the  pound  sterling  as  in  the  gold  dollar,  the  pound  sterling  is  worth 
4.8665  times  $1,  or  $4.8665.  The  mint  par  of  exchange  is  used  mainly  in 
determining  the  values  on  which  to  compute  customs  duties. 

442.  The    rate    of    exchange    is   the   market   value   in   one 
country  of  the  bills  of  exchange  on  another. 

The  price  paid  for  bills  of  exchange  fluctuates.  When  the  United  States 
owes  Great  Britain  exactly  the  same  amount  that  Great  Britain  owes  the 
United  States,  the  debts  between  these  countries  can  be  paid  without  the 
transmission  of  money,  and  exchange  is  at  par.  But  when  Great  Britain 
owes  the  United  States  a  greater  amount  than  the  United  States  owes 
Great  Britain,  exchange  in  the  United  States  is  at  a  discount  and  in  Great 
Britain  at  a  premium,  and  vice  versa.  The  rates  of  premium  or  discount 
are  limited  by  the  cost  of  shipping  gold  bullion  from  one  country  to  another. 
The  cost  of  shipping  gold  from  New  York  to  London  is  about  f  %.  There- 
fore, when  A  in  New  York  owes  B  in  London,  and  A  cannot  buy  a  bill  of 
exchange  on  London  for  less  than  $4.88^  to  $4.89,  it  is  cheaper  for  him  to 
export  gold.  On  the  other  hand,  if  D  in  London  owes  C  in  New  York  and 
C  cannot  sell  a  draft  on  D  for  more  than  $4.83|  to  $4.84,  it  is  cheaper  for 
him  to  import  gold.  The  greater  part  of  exchange  is  drawn  on  Great 
Britain,  France,  Germany,  Holland,  Belgium,  and  Switzerland.  Because 
London  is  the  financial  center  of  the  world,  probably  more  foreign  exchange 
is  drawn  on  Great  Britain  than  on  all  the  other  countries  combined. 

443.  Exchange   on   Great   Britain  is  usually  quoted  at  the 
number  of  dollars  to  the  pound  sterling ;    exchange  on  France, 
Belgium,  and  Switzerland,  at  the  number  of  francs  to  the  dollar  ; 
exchange  on  Germany,  at  the  number  of  cents  to  each  four  marks; 
exchange  on  Holland,  at  the  number  of  cents  to  each  guilder. 

The  accompanying  foreign  exchange  rates  were  quoted  recently. 

In    Great   Britain    3    da.   of  60  Days   Demand 

grace   are  allowed  on  all  bills      K^y;Veich;markV.V.:V.V.V:.:.V4^      *S8 
drawn  payable  after  sight,  but      France,  francs 5  i<;%      5 .15 

r   J  Belgium 5.18%        5.15% 

drafts  on  Great  Britain  payable      Switzerland,  francs B-18%      5.15% 

,      .    ,  ,  j   v  Holland,  guilders 40  40% 

at  sight  or  on  demand  have  no 

grace.     There  are  no  days  of  grace  allowed  on  any  drafts  drawn  on  Germany, 

and  nearly  all  Europe,  excepting  Holland,  where  1  da.  of  grace  is  allowed. 


EXCHANGE 


369 


j.  6000  M. 
k.  4000  M. 
1.  12000  M. 


WRITTEN  EXERCISE 

1.  Using  the  foregoing  table  of  quotations,  or  current  quota- 
tions clipped  from  any  daily  newspaper,  find  the  cost  of  de- 
mand drafts  for  each  of  the  following  amounts  : 

a.  £100.         d.    160  guilders.        g.    200  M. 

b.  £1200.       e.    240  guilders.        h.    160  M. 

c.  £1800.      /.    1200  guilders.      i.    2000  M. 

2.  Find  the  cost  of  a  60-da.  draft  for  each  of  the  amounts 
in  problem  1. 

WRITTEN  EXERCISE 

1.  F.  M.  Cole  &  Co.,  importers,  Boston,  owe  Richard   Roe, 
London,  £525  10s.,  6d.,  buy  by  check  the  draft  illustrated  on 
page  367,  and  remit  it  in  full  of  account.      If  exchange  on 
London  is  $4.87-J,  what  was  the  amount  of  the  check  ? 

2.  Jordan,  Marsh  &  Co.  wish  to  import  a  quantity  of  woolen 
goods  from  Bradford,  England.     They  make  up  an  order  and 
inclose   in   payment   the  following   draft  which  they  buy  by 
check,  at  $4.85^.     What  was  the  amount  of  the  check? 


MESS9?BROW^f,SHIHLEY*CO. 

^q.  3497 


3.  45  da.  before  the  draft  was  due  (problem  2)  John  Smith 
&  Co.  sold  it  to  Baring  Bros,  at  2%  discount.  How  much 
(in  English  money)  did  they  receive  ?  Write  the  indorsements 
which  would  appear  on  the  back  of  the  draft. 


370 


PRACTICAL   BUSINESS   ARITHMETIC 


4.  D.  M.  Knowlton  &  Co.  drew  the  following  commercial 
bill  of  exchange  and  sold  it  to  Kidder,  Peabody  &  Co.  at  96|. 
How  much  was  received  for  it  ? 


Commercial  bills  of  exchange  are  usually  drawn  by  exporters  against 
funds  abroad  which  have  accumulated  to  their  credit  from  sales  previously 
made.  The  exporter  generally  waits  until  the  rates  of  exchange  are  high 
and  then  draws  the  draft  as  above. 

5.  Aug.  1  T.  H.  Reed  &  Co.,  exporters,  Minneapolis,  Minn., 
bought  through  their  broker,  24,000  bu.  No.  1  wheat  at  84^  per 
bushel  and  paid  for  same  by  check.     What  was  the  amount  of 
the  check,  the  broker's  commission  being  J^  per  bushel  ? 

6.  Aug.  2  the  wheat  was  delivered  and   placed   with  City 
Elevator  for  storage.     The  storage  rates  were  |^  per  bushel  for 
the  first  10  da.  or  fraction  thereof,  and  -faf   per  bushel  for 
each  additional  day  thereafter.     On  Aug.  15  the  wheat  was 
withdrawn  from  the  City  Elevator  and  delivered  to  the  Soo 
Freight  Line  for  shipment  to  W.  B.  Radcliffe  &  Son,  Liver- 
pool.    What  was  the  amount  of  the  storage  bill  ? 

7.  The  wheat  was  sold  to  W.  B.  Radcliffe  &  Son  at  XI  12s. 
2d.  per  quarter  (8  bu.  or  480  lb.).     Make  out  the  bill  under 
date  of  Aug.  15. 

8.  On  Aug.  15  a  through  bill  of  lading  in  duplicate  was  re- 
ceived from  the  Soo  Freight  Line.     If  the  through  freight  rate 
from   Minneapolis  to   Liverpool    was   2d.   per   hundredweight, 
what  was  the  amount  of  the  freight  bill  ? 


EXCHANGE 


371 


9.  Aug.  16,  upon  presentation  of  the  bill  of  lading  to  the 
Western  Assurance  Co.,  the  goods  were  insured  for  10%  more 
than  their  billed  value  and  a  certificate  of  insurance  issued. 
What  was  the  amount  of  the  premium,  the  rate  being  \\%  ? 
10.  T.  H.  Reed  &  Co.,  drew  the  following  draft  on  W.  B. 
Radcliffe  &  Son  and  attached  it  to  the  bill  of  lading  and  cer- 
tificate of  insurance.  These  documents,  which  constitute  what 
is  called  a  documentary  bill  of  exchange,  were  then  offered  for 
sale  and  later  sold  to  Kidder,  Peabody  &  Co.,  at  the  rate  of 
$4.84|  per  pound.  How  much  was  received  for  the  bill? 


11.  Aug.    17    Kidder,  Peabody   &    Co.     sold    the    draft   to 
American  Express  Co.  at  f4.84J.     If  the  American  Express 
Co.  paid  by  check,  what  was  the  amount  of  the  check? 

12.  American  Express  Co.  forwarded  the  bill  to  Provincial 
Bank,  Liverpool,  for  collection,  and   this  bank  presented  the 
draft  to  W.  B.  Radcliffe  &   Son  for  acceptance.     Sept.   1  the 
wheat  arrived  by  steamer  and  as  the  draft  was  stamped  "Sur- 
render documents  only  upon  payment  of  draft"  W.   B.  Rad- 
cliffe &  Son  had  to  pay  the  draft  before  they  could  get  the  docu- 
ments or  the  goods.     As  the  draft  has  46  da.  yet  to  run,  the 
bank  allowed  W.  B.  Radcliffe  &  Son  1%  discount..     What  was 
the  amount  paid  by  W.  B.  Radcliffe  &  Son  ? 

Such  drafts  are  frequently  stamped  "  Surrender  documents  upon  accept- 
ance of  the  draft."  In  such  cases  the  documents  would  be  delivered  to  the 
consignee  upon  the  acceptance  of  the  draft,  and  he  could  then  obtain  pos- 
session of  the  goods. 


372 


PRACTICAL   BUSINESS   ARITHMETIC 


13.  What  was  T.  H.  Reed  &  Co.'s  net  gain  or  loss  on  the 
transactions  in  problems  5-10  ? 

LETTERS  OF  CREDIT  AND  TRAVELER'S  CHECKS 

444.  A  traveler's  letter  of  credit  is  an  instrument  issued  by  a 
banker  instructing  his  correspondents  in  specified  places  to  pay 
the  holder  funds  in  any  amount  not  exceeding  a  specified  sum. 


CIRCULAR  LETTER  OF  CREDIT. 


MESS?fBROWN,  S  H  i  PLEYS  Co. 

^^ 


^6^^<z^eU//u^ccA^ 
fmcucms 
e^tA^<^3^pC^ruc^^/<^n^ 


/u*^^ 


s^^ 


EXCHANGE 


373 


The  purchaser  of  a  letter  of  credit  is  required  to  subscribe  his  name 
upon  the  document  as  a  means  of  identification  later  on.  Other  copies 
of  the  signature  are  left  and  forwarded  to  the  leading  foreign  banks 
drawn  upon.  When  the  traveler  desires  funds,  he  presents  his  letter  to  the 
proper  bank  at  the  place  in  which  he  is  stopping.  The  letter  itself  always 
specifies  the  banks  that  will  honor  the  draft.  When  the  letter  is  presented 
to  a  foreign  banker  for  payment,  he  draws  a  sight  draft  on  the  London 
banker,  which  draft  the  traveler  is  required  to  sign.  If  the  signatures  on 
the  letter  and  on  the  draft  are  identical,  the  amount  desired  is  promptly  paid 
and  indorsed  on  the  back  of  the  letter.  The  indorsements  on  the  back 
of  a  letter  show  at  all  times  the  balance  available  for  the  traveler.  The 
bank  making  the  last  payment  retains  the  letter  to  send  to  the  drawee 
in  London.  Letters  of  credit  are  usually  drawn  payable  in  pounds  ster- 
ling, but  they  are  paid  in  the  current  money  of  the  country  in  which 
they  are  negotiated.  Banks  usually  charge  1%  commission  for  issuing 
a  letter  of  credit. 

445.  Another  instrument  frequently  used  by  travelers  is 
what  is  called  a  traveler's  check. 

/////M//////////////M////'/' 

AMERICAN  EXPRESS  COMPANY. 


When  a  check  is  purchased,  the  buyer  signs  his  name  in  the  upper  left- 
hand  corner.  When  he  wishes  funds,  he  presents  his  check  to  the  cor- 
respondent of  the  express  company  or  bank  and  signs  his  name  either 
in  the  upper  left-hand  corner  or  on  the  back  of  the  check.  On  the  form 
above,  he  would  sign  his  name  in  the  lower  left-hand  corner;  but 
on  the  form  on  page  374  he  would  sign  his  name  on  the  back.  The  lat- 
ter form  is  considered  better  because  it  is  more  difficult  to  forge  an- 
other's signature  when  there  is  no  signature  near  at  hand  from  which  to 
copy. 

The  terms  of  issue  are  cash  for  the  face  amount  plus  £%  commission. 


374 


PRACTICAL   BUSINESS   ARITHMETIC 


r  Five  PmmilH  Stevlliig.oi-  H*« 
the  order  of  lite  aU»ow 
iidorxod  with   ""  rtgunturi?. 


ORAL  EXERCISE 

1.  At  $4.85  to  the  pound  sterling  plus  1%  commission,  what 
did  the  letter  of  credit  on  page  372  cost? 

2.  At  the  same  rate,  find  the  cost  of  a  letter  of  credit  for 
£500;   £1000. 

3.  At   \°/o   commission,  what  will  be   the   total  cost  of  10 
checks   like   the   sample  on  page  373?    of  20  checks?     of    25 
checks  ? 

4.  At  $4.85  to  the  pound  plus  \  %  commission,  what  was  the 
cost  of  a  traveler's  check  on  page  374  ?     of  a  book  of  10  checks 
like  the  sample  on  page  374  ? 


WRITTEN  EXERCISE 

1.  On  the  letter  of  credit,  page  372,  the  following  payments 
are  recorded  on  the  back :  Aug.  31,  £  200 ;  Sept.  9,  £  400 ; 
Oct.  15,  £250;  Nov.  1,  £100;  Nov.  12,  £200.  The  holder 
returns  to  New  York  on  Nov.  20  and  presents  the  letter  to 
Brown  Brothers  &  Co.  for  the  refund.  At  $4.85  to  the  pound, 
how  much  will  Brown  Brothers  &  Co.  pay  on  the  letter? 

In  this  problem  it  is  assumed  that  Brown  Bros.  &  Co.  refund  1  %  commis- 
sion on  the  unused  portion  of  the  letter. 


EXCHANGE 


375 


2.  At  25^  per  word  and  1%  of  the  amount,  find  the  cost  of 
a  twenty-one  word  cable  money  order  from  Boston  to  Paris  for 
25,000  fr.  when  exchange  is  quoted  at  5.15|. 

Money  may  be  cabled  from  one  country  to  another  on  the  same  principle 
that  it  is  telegraphed  from  one  part  of  any  country  to  another  part.  In  a 
cable  message  a  charge  is  made  for  each  word  in  the  address  of  the  one  to 
whom  it  is  sent. 

WRITTEN  REVIEW  EXERCISE 

1.  A  broker  sold  for  me  a  bill  on  Manchester,  England,  at 
f  4.84J  and  charged  \%  brokerage.     What  was  the  face  of  the 
bill,  if  the  proceeds  were  $5218.50? 

2.  How  much  remains  in  the  bank  to  the  credit  of  H.  B. 
Claflin  &  Co.  after  the  following  check  was  issued  ? 


g)att  ^ZtS^rf.  /i  /a 


amnnnt,  $ 


3tjants  Crust  Company 


to  tfjc  orfcer  of 


3.  My  agent  in  Brussels,  Belgium,  purchased  for  me  carpet 
amounting  to  35,000  fr.,  and  his  commission  was  5%.     I  re- 
mitted him  a  draft  to  cover  the  cost  of   the    carpet   and  the 
commission  for  buying.     If  exchange  was  5.15|,  and  I  paid  for 
the  draft  by  check,  what  was  the  amount  of  the  check? 

4.  My  agent  in  Rotterdam  sold  for  me  525  kegs  of  tobacco, 
each  containing  50  lb.,  at  ^  guilder  per  pound,  and  charged 
me  a  commission  of  4^%.     I  drew  on  him  for  the  proceeds  and 
sold  the  draft  to  a  broker  at  40f .     If  the  broker  charged  \% 
for  his  services,  what  did  I  receive  as  proceeds  of  the  draft  ? 


EQUATIONS    AND   CASH  BALANCE 
CHAPTER   XXXI 

EQUATION  OF   ACCOUNTS 
ORAL  EXERCISE 

1.  How  long  will  it  take  $  5  to  produce  the  same  interest  as 
for  10  da.  ?     The  use  of  1 100  for  1  mo.  is  equivalent  to 

what  sum  for  2  mo.  ? 

2.  If  I  have  the  use  of  §50  of  A's  money  for  30  da.,  how 
much  of  my  money  should  he  have  the  use  of  for  15  da.   in 
return  for  the  accommodation  ? 

3.  The  interest  on  $40  for  2  mo.  plus  the  interest  on  140  for 
4  mo.  is  equal  to  the  interest  on  $80  for  how  many  months  ? 

4.  D  owes  E  $100;  $50  is  due  in  2  mo.  and  the  balance  in 
4  mo.     In  how  many  months  may  the  whole  be  paid  without 
loss  to  either  party  ? 

5.  On  Apr.  1  I  bought  a  bill  of  goods  amounting  to  $200, 
payable  as  follows:  $100  in  3  mo.  and  the  balance  in  5  mo. 
In  how  many  months  may  the  whole  sum  be  equitably  paid  ? 

6.  A  owes  B  $400  and  pays  $200  30  da.  before  the  account 
is  due.      How  long  after  the  account  is  due  may  B  have  in 
which  to  pay  the  balance  ? 

446.  The  process  of  finding  the  date  on  which  the  settle- 
ment of  an  account  may  be  made  without  loss  of  interest  to 
either  party  is  called  equation  of  accounts. 

Sometimes  one  or  more  of  the  items  in  a  personal  account  are  not  paid  at 
maturity  and  the  holder  of  the  account  suffers  a  loss ;  sometimes  one  or 
more  of  the  items  are  paid  before  maturity  and  the  holder  of  the  account 
realizes  a  gain.  To  equitably  adjust  these  items  of  loss  and  gain,  accounts 
are  equated.  Retail  accounts  are  not  often  equated ;  but  wholesale  and 
commission  accounts  are  frequently  equated,  particularly  foreign  ones. 

376 


EQUATIOK  OF  ACCOUNTS 


377 


447.  The  time  that  must  elapse  before  several  debts,  due  at 
different  times,  may  be  equitably  paid  in  one  sum  is  called  the 
average  term  of  credit;  the  date  on  which  payment   may   be 
equitably   made,    the  average  date   of    payment,    the   equated 
date,  or  the  due  date. 

448.  Any  assumed  date  of  settlement  with  which  the  several 
dates  in  the  account  are  compared  for  the  purpose  of  deter- 
mining the  actual  due  date  is  sometimes  called  the  focal  date. 

The  face  value  of  each  item  should  always  be  used  in  equating  accounts. 
Items  not  subject  to  a  term  of  credit  and  interest-bearing  notes  are  worth 
their  face  value  on  the  day  they  are  dated.  Items  subject  to  a  term  of 
credit  and  non-interest-bearing  notes  are  not  worth  their  face  value  until 
maturity. 

SIMPLE   ACCOUNTS 

ORAL  EXERCISE 

1.  If  I  owe  1200  due  Jan.  1  and  $400  due  Jan.  31,  when 
may  both  accounts  be  equitably  paid  in  one  sum? 

SOLUTION.  On  Jan.  31,  there  is  legally  due  $600  +  $  1  (the  interest  on  $200 
for  30  da.)-  Since  more  than  the  face  of  the  account  is  due,  the  equitable  date 
of  settlement  is  before  Jan.  31.  It  will  take  $600  one  third  as  long  as  $200  to 
produce  $  1  interest.  ^  of  30  da.  =  10  da.  The  whole  account  may  therefore 
be  paid  10  da.  before  Jan.  31,  or  Jan.  21,  without  loss  to  either  party. 

2.  You  sold  Baker,  Taylor  &  Co.  goods  as  follows  :  Apr.  20, 
$  600  ;  Apr.  30,  $  600.     How  much  is  legally  due  on  the  ac- 
count Apr.  30  ?  On  what  day  may  the  whole  account,  $  1200, 
be  paid  without  interest  ? 

3.  When  is  the  following  account  due  by  equation? 

A.  B.  COMER 


1907 

Sept. 

1 

To  mdse. 

300 

21 

To  mdse. 

300 

4.  Rowland  &  Hill  bought  goods  of  you  as  follows  :  Oct.  16, 
Oct.  31,  $  800.  How  much  was  legally  due  on  the  ac- 
count Oct.  31  ?  On  what  date  can  the  whole  of  the  account, 
$  1200,  be  paid  without  interest  ? 


378 


PRACTICAL   BUSINESS   ARITHMETIC 


449.   Example.     On  what  date  may  the  total  of  the  following 
account  be  paid  without  interest  ? 

F.  M.  PRATT  &  Co. 


1907 

Jan. 

1 

To  mdse.       20  da. 

30 

00 

9 

To  mdse.       10  da. 

120 

15 

To  mdse.       15  da. 

150 

21 

To  mdse.       10  da. 

300 

26 

To  mdse.       10  da. 

60 

DATE 
Jan.      1 

AMOUNT 

$30 

DAYS 

25 

INTEREST 

$.125 

9 

120 

17 

.34 

15 

150 

11 

.275 

21 

300 

5 

.25 

26 

60 

0 

SOLUTION.  Take  the  latest  date, 
Jan.  26,  as  the  focal  date.  If  settle- 
ment was  made  on  Jan.  26,  the 
holder  of  the  account  might  charge 
interest  on  each  item  as  shown  in 
the  accompanying  statement. 

The  holder  loses  $  0. 1 1  per  day 
as  long  as  the  account  remains  un- 
settled. If  settlement  was  made 
Jan.  26,  the  loss  would  be  f  0.99,  or 
9  days'  interest;  therefore  if  the  ac- 
count were  settled  9  da.  before  Jan. 
26,  the  holder  would  lose  nothing. 

PROOF.  The  proof  of  the  problem  must  show  that  the  interest  on  the  items 
dated  before  Jan.  17,  the  equated  date,  is  offset  by  the  discount  on  the  items 
dated  after  Jan.  17.  The  following  items  are  dated  before  Jan.  17  : 


1.99 

The  amount  of  the  account  =  $  660. 
The  interest  on  $660  for  1  da.  =  $0.11. 
$  0.99  -f-  $  0.11  =  9,  or  the  number  of  days. 
Jan.  26— 9  da.  =Jan.  17,  the  equated  date. 


DATE 

Jan.    1  to  17 

9  to  17 

15  to  17 


INTEREST 
PERIOD 

16  da. 


ITEM 
$30 
120 
150 


INTEREST 
$.08 
.16 
.05 


The  following  items  are  dated  after  Jan.  17 


Total  interest,  $.29 


DATE 

Jan.  17  to  21 
17  to  26 


DISCOUNT 
PERIOD 

4  da. 
9 


ITEM 
$  300 
60 


DISCOUNT 
•$.20 
.09 


Total  discount,  $  .29 


The  proof  shows  that  the  equated  date,  Jan.  17,  is  correct. 

Any  rate  of  interest  may  be  used  in  equating  an  account.  As  a  matter 
of  convenience,  always  use  6  %.  If  items  are  subject  to  terms  of  credit,  add 
the  time  to  the  date  of  the  items  before  beginning  to  equate. 


EQUATION   OF  ACCOUNTS 


379 


WRITTEN  EXERCISE 


In  each  of  the  following  problems  find  the  equated  date    and 
prove  the  work.     Assume  that  all  the  dates  are  in  1907 . 


1.    F.  M.  Drake,  Dr. 

Mar.  2,  To  mdse.     .     .    f  120. 

8,  To  mdse.     .     .      180. 
11,  To  mdse.     .     .        60. 
17,  To  mdse.     .     .      240. 

23,  To  rndse.     .     .      150. 
3,    Geo.  M.  Barton,  Dr. 
Aug.  3,  To  mdse.,  60  da.  1360. 

6,  To  mdse.,  30  da.     240. 

11,  To  mdse.,  30  da.      300. 

19,  To  mdse.,  30  da.        60. 

24,  To  mdse.,  30  da.     180. 
5.    Carter  &  Co.,  Dr. 

May  5,  To  mdse.     .     .    #180. 

12,  To  mdse.     .     .      300. 

16,  To  mdse.     .     .      230. 

20,  To  mdse.     .     .      270. 

23,  To  mdse.     .     .      360. 
7.    Brigham  &  Co.,  Dr. 

Sept.  4,  To  mdse.,  60  da.  1600. 

9,  To  mdse.,  60  da.     450. 

12,  To  mdse.,  60  da.     350. 

17,  To  mdse.,  60  da.     400. 
22,  To  mdse.,  30  da.     500. 

30,  To  mdse.,  net,     .    150. 
9.    Brown,  Kerr  &  Co.,  Dr. 
Oct.  1,  To  mdse.,  3  mo.  $210. 

5,  To  mdse.,  60  da.    840. 

13,  To  mdse.,  60  da.    720. 

21,  To  mdse.,  60  da.    660. 

24,  To  mdse.,  60  da.    540. 

31,  To  rndse.,  net,     .   300. 


2.    Louis  M.  Allen,  Dr. 
Apr.  3,  To  mdse.     .     .    1160. 
9,  To  mdse.     .     .       250. 

13,  To  mdse.     .     .       100. 

19,  To  mdse.     .     .      280. 

23,  To  mdse.     .     .      420. 
4.    Leon  H.  Hazelton,  Dr. 
June  6,  To  mdse.     .     .    $200. 

9,  To  mdse.     .     .      300. 

14,  To  mdse.     .     .      400. 

24,  To  mdse.     .     .      600. 

27,  To  mdse.     .     .      330. 
6.  Lamson  &  Roe  Co.,  Dr. 
Dec.  1,  To  mdse.,  3  mo.  1 294.20. 

10,  To  mdse.,  3  mo.    698.40. 

20,  To  mdse.,  60  da.  136.60. 

24,  To  mdse.,  60  da.  740.60. 
28,  To  mdse.,  60  da.  700.40. 

8.    D.  H.  Beckwith  &  Co.  Dr. 
Nov.  3,  To  mdse.,  2  mo.  1 750.50. 
8,  To  mdse.,  2  mo.    432.25. 

17,  To  mdse.,  net,      275.50. 

22,  To  mdse.,  2  mo.    210.50. 

25,  To  mdse.,  1  mo.    168.30. 

28,  To  mdse.,  lino.    240.50. 
10.    D.  M.  Smith  &  Co.,  Dr. 


July  3,  To  mdse. 
8,  To  mdse. 
11,  To  mdse. 
16,  To  mdse. 
25,  To  mdse. 
29,  To  mdse. 


1420.30. 
325.70. 
417.25. 
186.24. 
240.60. 
126.84. 


380 


PRACTICAL   BUSINESS   ARITHMETIC 


COMPOUND   ACCOUNTS 

ORAL  EXERCISE 

l.    The  following  is  your  account  with  John  D.  Foster. 


Had  no  payment  been  made,  when  would  the  account  have  been  due? 
Since  no  payment  was  made  until  after  maturity,  you  have  /os/  the  use 
of  $  400  for  how  many  days  ?  To  offset  this  loss  what  should  be  the  date  of 
an  interest-bearing  note  given  to  cover  the  balance  of  the  account?  Jan. 
16  —  30  da.  =  Dec.  ?,  the  date  of  an  interest-bearing  note  given  to  cover 
the  balance  of  the  account. 

2.    The  following  is  your  account  with  Walter  H.  Wood. 
WALTER  H.  WOOD 


1907 

Apr. 

1 

To  mdse.,30da. 

600 

III    19°7  1 
00     Apr.  |  16 

By  Cash 

300 

00 

Had  no  payment  been  made,  when  would  the  account  have  matured? 
By  the  payment  recorded  you  have  gained  the  use  of  $300  for  how  many 
days  ?  To  offset  this  gain,  you  should  allow  Walter  II .  Wood  to  keep  the 
balance  of  the  account  how  many  days  after  maturity?  May  1  +  15  da. 
=  May?,  the  date  on  which  the  balance  is  equitably  due. 

3.  May  1  B  sold  C  goods  amounting  to  $  500.     Terms  :     30 
da.     May  11  C  made  a  payment  of   1250  on    account.      On 
what  date  is  the  balance  of  the  account  due  ? 

4.  Find  the  date  of  an  interest-bearing  note  given  for  the 
balance  of  each  of  the  following  accounts,  assuming  that  the 
terms  in  each  case  are  30  da.;  assuming  that  the  terms  are  cash. 


NAME 

a.  H.  H.  Howard 

b.  W.  H.  Lyman  &  Co. 

c.  R.  H.  Delaney  &  Son 


DR. 

Jan.  1,  1400 
Jan.  1,  1 400 
Jan.  1,  1400 


CB. 

Jan.  16,  $  300 
Jan.  16,  $  100 
Jan.  16,  $  200 


EQUATION   OF   ACCOUNTS  381 

450.    Examples.    1.    Find  the  equated  date  for  the  following  : 


/    L 

44   * 


24=0 


/f 


SOLUTION.   Take  as  focal  date  the  latest  date  in  the  account,  Feb.  24. 

DEBITS 


DATE 
Feb.  1 
14 


DATE 

Feb.  18 
24 


ITEMS 

$360 

240 

$600 


ITEMS 
$180 

180 
$360 


CREDITS 


INTEREST 
PERIODS 

23  da. 
10 


INTEREST 
PERIODS 

6  da. 
0 


INTEREST 
$1.38 
.40 

$1.78 


INTEREST 
$.18 
.00 
$.18 


$  600  -  $  360  =  $  240,  the  balance  of  the  account.  $  1.78  -  $  .18  =  $  1.60, 
the  interest  due  the  holder  of  the  account  on  Feb.  24.  The  interest  on  $240 
for  1  da.  =  $0.04.  $  1.60  -^  $0.04  =  40,  the  number  of  days.  If  the  account 
were  settled  Feb.  24  there  would  be  interest  for  40  da.  due  the  holder  of  it. 
Therefore  the  balance  of  the  account  is  due  40  da.  before  Feb.  24.  Feb.  24  — 
40  da.  =  Jan.  15,  the  equated  date. 

PROOF.  To  prove  the  correctness  of  the  above  work  it  is  necessary  to  show 
that  a  payment  of  $  240  on  Feb.  24  will  result  in  no  loss  of  discount  to  either 
party.  This  may  be  done  by  equatingthe  account,  using  Jan.  15  as  the  focal  date. 

DEBITS 


DATE 
Jan.  15  to  Feb.  1 


15  to 


14 


DATE 

Jan.  15  to  Feb.  18 
15  to  24 


DISCOUNT 
PERIODS 

17  da. 
30 


CREDITS 

DISCOUNT 
PERIODS 

34  da. 
40 


ITEMS 

$360 

240 

$600 


ITEMS 

$180 

180 

$360 


DISCOUNT 

$1.02 
1.20 

$2.22 


DISCOUNT 

$1.02 

1.20 

$2.22 


As  there  is  no  difference  between  the  debit  discount  and  the  credit  discount, 
the  account  is  proved  to  be  due  by  equation  on  Jan.  15,  1907. 


382  PRACTICAL   BUSINESS   ARITHMETIC 

2.    Find  the  equated  date  for  the  following  account : 


Assume  May  31  to  be  the  date  of  settlement. 


DATE 

Apr.  1 
24 
30 


DEBITS 

TERM  OF 
CREDIT 

MATURITY               ITEM 

60  da. 

May  31            $660 

30 

24               360 

10 

10               280 

$1300 


CREDITS 


DATE 

May  2 
20 


ITEM 

$330 

300 

$630 


INTEKKST 
PERIOD 

29  da. 
11 


INTEREST 
PERIOD 

Oda. 


21 


INTEREST 

$1.595 

.55 
$2.145 


JJ  0 

J  00 


INTEREST 

$.00 

.42 

.98 

$  1 .40 


$  1300  -  $630  =  $(570,  the  balance  of  the  account.  $  2.145  -  $  1.40  =  $0.745, 
the  interest  due  Watson  &  Moore  on  May  31.  The  interest  on  $670  for  1  da.  = 
$0.111.  $0.745  -4-  $0.11£  =  6.6  or  7,  the  number  of  days.  If  the  account  were 
settled  May  31,  Watson  &  Moore  might  deduct  $0.75  from  the  balance  of  the  ac- 
count ;  therefore  the  balance  of  the  account  is  not  due  until  7  da.  after  May  31, 
or  June  7,1907. 

PROOF.     The  maturity  of  each  item  is  used  in  the  proof. 


DATE 

May  31  to  June  7 

24  to  7 

10  to  7 


DATE 

May  2  to  June  7 
20  to  7 


DEBITS 

INTEREST 
PERIOD 

7  da. 
14 

28 

CREDITS 

INTEREST 
PERIOD 

36  da. 
18 


ITEM 


360 

280 


$1300 

ITEM 

$330 
300 
$630 


INTEREST 

S  -77 
.84 
1.307 
$2.917 


INTEREST 
$1.98 

.90 


$2.88 

$2.917  -  $2.88  =  $0.037  ;  as  this  is  less  than  the  interest  on  the  balance  of 
the  account  for  |  da.  the  solution  is  probably  correct. 


EQUATION   OF   ACCOUNTS 


383 


WRITTEN  EXERCISE 

Find  the  equated  date  and  prove  the  work: 
i.  FRED  L.  UPSON 


1907 

11907 

Jan. 

10 

To  mdse. 

360 

Jan. 

25 

By  cash 

180 

30 

To  mdse. 

240 

Feb. 

12 

By  cash 

120 

2. 


VINTON  L.  BROWN  &  Co. 


1907 

1907 

Mar. 

11 

To  mdse. 

420 

Mar. 

27 

By  cash 

540 

23 

To  mdse. 

300 

31 

By  cash 

180 

Apr. 

6 

To  mdse. 

300 

Apr. 

24 

By  cash 

300 

20 

To  mdse. 

120 

3. 


ANSON  L.  JAMES 


1907 

1907 

Mar. 

8 

To  mdse.,  10  da. 

240 

60 

Mar. 

18 

By  cash 

240 

60 

12 

To  mdse.,  10  da. 

180 

30 

24 

By  30-da.  note 

19 

To  mdse.,  10  da. 

246 

with  interest 

300 

29 

To  mdse.,  10  da. 

381 

24 

31 

By  cash 

257 

54 

The  charge  under  Mar.  8  was  paid  when  due,  Mar.  18. 
be  omitted  in  equating  the  account. 

4.  MACGREGOR    &    Co. 


Such  items  may 


1907 

1907 

Apr. 

7 

To  mdse.,  10  da. 

127 

54 

Apr. 

17 

By  cash 

127 

54 

25 

To  mdse. 

218 

99 

30 

By  cash 

100 

May 

6 

To  mdse.,  10  da. 

87 

43 

May 

16 

By  cash 

206 

42 

18 

To  mdse. 

150 

24 

By  mdse. 

35 

20 

27 

To  mdse.,  10  da. 

86 

45 

5. 


DAVID  J.  UPHAM 


1907 

1907 

June 

7 

To  mdse. 

128 

50 

June 

14 

By  cash 

332 

50 

10 

To  mdse. 

432 

75 

25 

By  mdse. 

67 

40 

15 

To  mdse. 

78 

55 

30 

By  cash 

248 

60 

21 

To  mdse. 

246 

80 

July 

15 

By  cash 

500 

29 

To  mdse. 

312 

30 

28 

By  mdse. 

88 

54 

July 

3 

To  mdse. 

186 

40 

14 

To  mdse. 

66 

36 

384 


PEACTICAL   BUSINESS   ARITHMETIC 


ACCOUNT   SALES 

451.  The  method  of  averaging  an  account  sales  is  practically 
the  same  as  the  method  of  averaging  an  ordinary  ledger  ac- 
count. The  charges  for  freight,  commission,  guaranty,  etc., 
constitute  the  debits  and  the  sales  the  credits  of  the  account. 

Commission  and  guaranty  are  sometimes  considered  due  on  the  date  of 
the  last  sale,  and  sometimes  on  the  average  date  of  the  sales.  When  goods 
are  sold  promptly,  commission  and  guaranty  are  generally  considered  due  on 
the  date  of  the  last  sale ;  when  the  sales  are  large  and  there  are  long  intervals 
between  them,  commission  and  guaranty  are  generally  considered  due  on 
the  average  due  date  of  the  sales.  When  goods  are  sold  for  cash,  the  ac- 
count sales  is  seldom  averaged. 

WRITTEN   EXERCISE 

1.  Equate  the  account  sales  on   page    267,    assuming   that 
both  sales  were  made  on  30  days'  time,  and  that  the  commission 
is  due  on  the  date  of  the  last  sale. 

2.  Copy  and  complete  the  following  account  sales.     Consider 
the  commission  as  due  on  the  date  of  the  last  sale. 


for  tl)e 


,  J&.JB.,       July  3. 
Of  Wentworth,  Stratton  &  Co. 


10 


Indianapolis.  Ind. 


Commifigion 


June 

8 

295  bbl.  Roller  Process  Flour,  60da.  $5.75 

**•** 

** 

12 

315  *'  Old  Grist  Mill  Flour,  Cash    5.45 

#*** 

*# 

July 

1 

305  "  Roller  Process  Flour,  60  da.   5.671/2 

**** 

** 

3 

285  "  Old  Grist  Mill  Flour,  30  da.  5.75 

#**# 

** 

June 

12 

(3Efrar0e£ 

Freight  and  cartage 

112 

50 

9 

Insurance 

60 

July 

3 

Storage 

30 

3 

Commission.  5%  of  sales 

*** 

** 

* 

Net  proceeds  due  by  equation 

•  •  •  • 

** 

**** 

** 

**** 

** 

CHAPTER  XXXII 
CASH  BALANCE 

ORAL  EXERCISE 

l.    When  is  the  balance  of  the  following  account  due  ? 
JAMES  B.  SWEENEY 


1907 

Jan. 

1 

To  mdse.,  30  da.        |  600 

P907 
an. 

31 

By  cash 

300 

00 

2.  If  no  interest  is  charged  on  overdue  balances,  how  much 
will  settle  the  account  Feb.  28  ? 

3.  If  interest  at  6%  is  charged  on  all  amounts  not  paid  at 
maturity,  what  is  the  cash  balance  of  the  above  account  Feb.  28  ? 

4.  Assuming  that  interest  is  charged  on  amounts  not  paid 
at  maturity,  find  the  cash  balance  of  the  above  account  March 
30,  at  6%. 

452.  The  amount  due  upon  an  account  at  any  given  time  is 
called  the  cash  balance  of  an  account. 

When  interest  is  not  charged  and  discount  is  not  allowed,  the  cash 
balance  is  the  difference  between  the  sides  of  an  account.  When  interest  is 
charged  and  discount  is  allowed,  the  cash  balance  is  the  difference  between 
the  sides  of  an  account  after  interest  has  been  added  to  overdue  items  and 
discount  deducted  from  items  not  yet  due. 

Whether  or  not  interest  or  discount  is  charged  or  allowed  on  ledger 
accounts  is  determined  by  custom  or  agreement.  It  is  customary  for 
wholesalers  to  charge  interest  on  all  overdue  accounts.  As  a  rule,  retailers 
do  not  charge  interest  on  the  items  of  an  overdue  account,  but  they  fre- 
quently close  personal  accounts  at  the  end  of  the  year  and  charge  interest 
on  the  balances  brought  down  from  the  date  of  closing  to  the  date  of 
settlement. 

453.  Example.     What  is  the  cash  balance  of  the  following 
account   Aug.   1,    1907,    interest  being   charged   on   overdue 
amounts  at  the  rate  of  6  %  ? 

385 


386 


PRACTICAL   BUSINESS   ARITHMETIC 


//        /a 

*        /o 


£00 
J  0  0 


SOLUTION. 


DEBITS 

DATE 

TERM  OF 
CREDIT 

MATURITY 

ITEM 

lp™™> 

June  1 

30  da. 

July     1 

$900 

31  da. 

9 

10 

June  19 

450 

43 

20 

10 

30 

300 

32 

INTEREST 

$4.65 
3.23 
1.60 


$1650 


CREDITS 


DATE 
June  30 
July  10 
18 


ITEM 

$600 

300 

150 

$1050 


INTEREST 
PERIOD 

32  da. 
22 

14 


$9.48 


$3.20 

1.10 

.35 

$4.65 


The  debit  footing  and  interest :  $  1650  +  $9.48  =  $  1659.48 

The  credit  footing  and  interest :  $  1050  +  $  4.65  =  81054.65 

The  balance  due  Aug.  1,  1907  =  $   604.83 

WRITTEN    EXERCISE 

1.  Find  the  cash  balance  due  June  1,  1907,  on  problem  4, 
page  383,  money  being  worth  5  %. 

2.  Equate  the  following  account  and  find  the  cash  balance 
due  Aug.  1,  1907,  money  being  worth  4|%. 

FREDERICK  T.  LAWRENCE 


1907 

lyuT 

May 

4 

To  mdse.,  60  da. 

1360 

May 

14 

By  cash 

360 

17 

To  mdse.  ,  30  da. 

720 

June 

10 

By  cash 

300 

26 

To  mdse.,  60  da. 

1080 

21 

By  cash 

420 

To  find  the  cash  balance  of  an  equated  account :  Equate  the  account. 
Compute  the  interest  on  the  balance  of  the  account  fr.om  the  equated  date  to  the 
date  of  settlement.  Add  the  interest  to  the  balance  of  the  account  and  the  result 
is  the  cash  balance  due. 


CASH  BALANCE 


387 


3-6.    The  following  is  a  page  from  a  sales  ledger.     Find  the 
cash  balance  due  on  each  account  Aug.  1,  money  being  worth  6  % . 


'f'7 

/iff  7 

??t<zy 

^ 

~/s0->ms0&id~£s./O'i}£ets- 

^ 

3  60 

— 

%Z^ 

/# 

~&n/st>et^&' 

^ 

360 

— 

'7 

t?           ft           J>     » 

J/6 

720 

— 

'1 

tt         tt 

^ 

J  00 

— 

Zt 

»         n          tt    // 

J*r 

/  <?<P0 

z/ 

//         // 

&/OJ 

t/2.0 

^^^ 


'000. 


/fff 


/  000 


30 


//          /»          ft 


/zoo 


&J0 


2.0 


'  Z00 


DIVIDENDS    AND    INVESTMENTS 
CHAPTER   XXXIII 

STOCKS  AND  BONDS 

STOCKS 

454.  A  corporation  or  stock  company  is  an  artificial  person 
created  by  law  or  under  the  authority  of  law  for  an  association 
of  individuals. 

Being  a  mere  creature  of  law  a  corporation  possesses  only  those  properties 
which  its  charter  (the  instrument  which  defines  its  rights  and  duties)  confers 
upon  it.  These  are  such  as  are  best  calculated  to  effect  the  object  for  which 
it  was  created.  Among  the  most  important  are  legal  immortality  and  power 
to  act  as  a  single  person. 

455.  The  capital  stock  of  a  corporation  is  the  amount  con- 
tributed by  the  stockholders  to  carry  on  the  business.     A  share 
is  one  of  the  equal  parts  into  which  the  capital  stock  is  divided. 

Shares  of  $100  are  the  rule  in  most  companies,  although  there  are  some 
exceptions.  Reading  Railroad  stock,  for  instance,  is  divided  into  shares  of 
$  50  each.  Mining  companies  rather  more  often  use  other  amounts  than 
$100. 

456.  A  stock  certificate  is  an  instrument  signed  usually  by 
the  president  and  treasurer  of  the  company  specifying  that  the 
holder  is  the  owner  of  a  certain  number  of  shares  of  stock  in 
the  corporation.     A  stockholder  is  a  person  who  owns  one  or 
more  shares  of  stock. 

Stockholders  elect  a  few  of  their  number  to  have  general  control  of  the 
company.  These  constitute  a  board  of  directors,  which  is  in  turn  controlled 
by  an  executive  committee.  This  executive  committee  is  again  controlled 
by  a  capitalist,  who  holds  more  of  the  stock  than  any  other  person.  The 
average  stockholder  carries  his  stock  merely  for  dividends  and  leaves  the 
burden  of  the  management  to  the  directors. 


STOCKS  AND  BONDS 


389 


457.  A  dividend  is  a  sum  paid  to  the  stockholders  out  of  the 
net  earnings  of  the  company.     An   assessment  is  a  sum  levied 
upon  stockholders  to  make  up  losses  or  deficiencies. 

The  board  of  directors  decide  upon  the  rate  of  dividend,  which  is  fre- 
quently an  even  per  cent  on  the  face  value  of  the  slock  of  the  corporation. 
If  fractions  are  used  in  these  rates,  they  are  usually  halves  or  fourths.  Any 
portion  of  the  profits  remaining  on  hand  after  dividends  have  been  declared 
is  usually  credited  to  undivided  profits,  an  account  which  is  opened  to  receive 
amounts  set  aside  to  be  used  in  an  emergency  or  in  any  manner  which  may 
be  determined  by  the  directors.  Some  corporations,  notably  national  banks, 
carry  a  portion  of  the  net  profits  to  a  surplus  fund  before  declaring  dividends. 
This  fund,  with  certain  restrictions,  may  be  used  in  practically  the  same 
manner  as  the  undivided  profits  account. 

Shares  of  stock  may  be,  and  frequently  are,  non-assessable. 

458.  The  two  leading  kinds  of  stock  are  preferred  and  common. 

459.  Preferred  stock  is  stock  which  entitles  the  holder  to  a 
fixed  rate  of  dividend  which  must  be  paid  before  anything  can 
be  divided  among  the  stockholders. 


ICORPOKATBD.VNDBR  THE  LAVS  OF  TBB  COMMONWEALTH  OF  MASSACHUSETTS. 

SHARES.  $roo  EACH. 


390 


PRACTICAL   BUSINESS   ARITHMETIC 


460.  Common  stock  is  stock  which  entitles  the  owner  to  an 
equal  proportionate  share  of  the  net  earnings  of  the  company 
after  the  dividends  on  the  preferred  stock  have  been  paid. 

Preferred  stock  is  usually  bought  for  investment  and  common  stock  for 
speculation.  But  many  companies  have  no  preferred  stock,  and  their  com- 
mon stock  is  so  steadily  a  dividend  payer,  and  thus  so  valuable,  that  it  is  not 
considered  a  speculative  commodity.  Preferred  stock  is  usually  given  to 
secure  some  obligation  of  the  company  or  to  meet  some  special  demand  for 
capital  when  common  stock  may  not  be  disposed  of  to  advantage. 


INCORPORATED  UNDER  THE  LAWS  OF  THE  COMMONWEALTH  OF  MASSACHUSETTS. 

SHARES.  $;oo  EACH. 


461.  The  par  value  is  the  face  value  of  stocks;  the  market 
value  is  the  sum  for  which  the  stocks  can  be  sold  in  the  market. 

462.  If  a  company  is  prosperous  and  pays  a  higher  rate  of 
dividend  than  the  money  could  earn  in  other  ways,  a  share  may 
sell  for  more  than  its  face  value.     The  stock  is  then  said  to  be 
above  par,  or  at  a  premium.     If  the  company  is  not  prosperous 
and  pays  a  lower  rate  of  dividend  than  could  be  earned  on  the 
money  in  other  ways,  a  share  may  sell  for  less  than  its  face 
value.     The  stock  is  then  said  to  be  below  par,  or  at  a  discount. 


STOCKS   AND   BONDS  391 

463.  A  stock  broker  is  a  person  who  negotiates  sales  of  stock. 
Brokerage    is    a    commission    charged    by    a  stock  broker   for 
buying  and  selling  securities. 

Stocks  are  usually  bought  and  sold  through  stock  brokers.  Brokerage  is 
usually  £%  of  the  par  value  of  the  stock;  a  charge  is  also  made  both  for 
buying  and  for  selling. 

464.  When  the  price  of  stock  is  quoted  at  97,  118f,  160-|, 
it  means  that  a  share  whose  par  value  is  $  100  can  be  bought 
for  $97,  1118.75,  $160.50.     If  a  person  buys  stock  through  a 
broker  at  1601,  it  will  cost  him  $160.50  +  $0.121  brokerage,  or 
$160.62|;  if  he  sells  stock  through  a  broker  for  1601,  he  will 
receive  as  proceeds  $160.50  -  $0.121,  or  $160.371. 

Fractions  in  stock  quotations  are  always  halves,  fourths,  or  eighths,  and 
fractions  of  a  share  cannot  be  purchased.  The  bulk  of  the  transactions  in 
the  stock  exchange  are  in  100-share  lots,  although  smaller  lots  are  often 
purchased  for  investment. 

ORAL    EXERCISE 

1.  Examine  the  certificate  of  stock,  page  389.     What  is  the 
name  of  the  company?     From  whom  did  the  company  get  its 
right  to  carry  011  business  as  a  corporation  ? 

2.  What  is  the  entire  capital  stock  of  the  company  ?     Into 
how  many  shares  is  this  divided  ?     What  per  cent  of  the  entire 
stock  of  the  company  does  the  holder  of  the  certificate  own? 

3.  What   kind   of   stock   is  represented  by  the  certificate  ? 
What  is  the  difference  between  common  and  preferred  stock? 

4.  What   is   the   par  value  of  each  share  ?     If  the  market 
value  of  each  share  is  $160,  what  is  the  certificate  worth? 

5.  What   sum    must  be  laid  aside  to  provide  for  the    divi- 
dends on  the  preferred  stock  of  the  company,  the  rate  being  6  %  ? 
How  much  of  this  sum  will  the  holder  of  the  certificate  receive  ? 

6.  Examine  the  stock  certificate,  page  390.      What  part  of 
the  stock  of  the  company  is  common  stock  ? 

7.  A  5%  dividend  on  the  common  stock  would  require  how 
much  money  from  the  treasury  of  the  company  ?     Of  this  sum 
how  much  would  George  W.  Putnam  receive  ? 


392  PRACTICAL   BUSINESS   ARITHMETIC 

DIVIDENDS  AND  ASSESSMENTS 
WRITTEN  EXERCISE 

Unless  otherwise  specified  the  par  value  of  a  share  will  be  understood  to 
be  $100. 

1.  A  company  with  $3,500,000  capital  declares  an  8  %  divi- 
dend.    What  does  the  holder  of  250  shares  receive  ? 

2.  B   holds   450    shares   of    Pennsylvania   Railroad   stock. 
When  the  company  declares  a  dividend  1%%,  how  much  will 
he  receive  ? 

3.  What  annual  income  is  derived  from  investing  $  48,000 
in  Union  Pacific  Railroad  stock  at  120,  if  2|  %  semiannual  divi- 
dends are  declared  ? 

4.  E.  H.  Rhodes  holds  600  shares  of  Leliigli  Valley  Railroad 
stock.     If  he  received  the  following  check  as  his  annual  divi- 
dend, what  was  the  rate  ? 


/9 


Zfirst  ^lationat  SBank 

|0/J 


QividendJfo. 

'/reasurer 


5.  A  company  with  §1,000,000    capital    declares   quarterly 
dividends  of  \\%.     What  are  the  annual  dividends?     What  is 
the  amount  received  annually  by  D,  who  owns  475  shares  ? 

6.  A   corporation  with   a  capital  of  $125,000  loses  $2500. 
What  per  cent  of  his  stock  must  each  stockholder  be  assessed 
to  meet  this  loss?     How  much  will  it  cost  A,  who  owns  150 
shares  ? 

7.  A  company  with  a  capital  of  $  750,000  declares  a  semi- 
annual dividend  of  3^%.     How  much  money  does  it  distribute 
among  its  stockholders  annually?      What  is  the  annual  income 
of  a  man  who  owns  200  shares  ? 


STOCKS   AND   BONDS  393 

8.  If  the  Reading  Railroad  declares  a  semiannual  dividend 
of  2|  %  011  a  capital  stock  of  $500,000,000,  what   amount   is 
annually  distributed  among   the  stockholders  ?     What  is   the 
annual  income   to   J.   P.   Morgan  from   this  stock  if  he  owns 
7,500,000  shares  having  a  par  value  of  $50  each? 

9.  During  a  certain  year  a  manufacturing  concern  with 
a  capital  of  %  750,000  earns  175,500  above  all  expenses.      It 
decides  to  save  $15,500  of  this  for  emergencies  and  to  divide 
the  remainder  in  dividends.      What  is  the  rate  ?     What  would 
be  the  amount  of  A's  dividend  check  if  he  owns  125  shares  ? 

10.  The  capital  stock  of  the  Gramercy  Finance  Company  is 
$1,500,000.     The  gross  earnings  of  the  company  for  a  year  are 
$875,000  and  the  expenses  $215,000.      What  even  per  cent  of 
dividend  may  be  declared  and  what  would  be  the  amount  of 
undivided  profits  if  10  %  of  the  net  earnings  are  first  set  aside 
as  a  surplus  fund  ? 

11.  A   railway  company   has  a  capital   of   $3,500,000   and 
declares   dividends    semiannually.       During   the   period   from 
Jan.  1  to  July  1  of  a  certain  year  the  net  earnings  of  the  com- 
pany were  $191,000.     Of  this  amount  10  %  is  carried  to  surplus 
fund.    What  even  rate  per  cent  of  dividend  may  be  declared  on 
the  balance  and  how  much  will  be  carried  to  undivided  profits  ? 

12.  A  company  with  a  capital  stock  of  $500,000  gains  during 
a  certain  year  $38,750.     It   decides   to   carry   $5000    of   the 
profits  to  surplus   fund  and  to   declare   an  even  per  cent  of 
dividends  on  the  remainder.       What  sum  was  divided  among 
the  stockholders,   and    what  sum    was   carried    to    undivided 
profits  account  ?     What  was  the  annual  income  to  F  from  this 
stock  if  he  owned  500  shares  ? 

13.  During  a  certain  year  the  gross  earnings  of  a  railroad 
having  a  capital  stock  of  $100,000,000  were  $65,150,000,  and 
the  operating  expenses  $45,150,000.     If  the  company  declared 
a  semiannual  dividend  of  3|  %  and  carried  the  balance  of  the 
net   earnings   to    undivided   profits   account,    how   much   was 
divided  among  the  stockholders  ?    How  much  was  the  working 
capital  of  the  company  increased  ? 


394 


PRACTICAL   BUSINESS   ARITHMETIC 


14.  The  capital  stock  of  the  National  Shawmut  Bank 
is  §8,000,000,  and  dividends  are  declared  semiannually. 
The  profits  of  the  bank  for  a  certain  six  months  are  f  185,750. 
10  %  of  this  sum  is  carried  to  a  surplus  fund.  The  directors 
then  vote  to  declare  a  dividend  of  3^  %  and  carry  the  balance 
of  the  profits  to  undivided  profits  account.  What  amount  was 
carried  to  surplus  fund  account  ?  to  dividend  account  ?  to 
undivided  profits  account  ? 

BUYING  AND  SELLING  STOCK 

465.  The  following  is  an  abbreviated  form  of  the  stock 
quotations  for  a  certain  day  on  the  New  York  Stock  Exchange: 

TABLE  OF  SALES  AND  RANGE  OF  PRICES 


Sales 

Stocks 

3  pen. 

High. 

Low. 

Clos. 

Net 
Changes 

100 

Adams  Express 

243 

243 

243 

243 

+     % 

123,500 
49,500 

Amalgamated  Copper 
Am.  Sugar  Kef. 

81 
151 

81% 
152 

79% 
149% 

79% 
150 

4-1     * 

100 

Am.  Sugar  Kef.  pfd. 

141 

141 

141 

141 

+   1 

9,300 
12,900 
1,600 

Baltimore  &  Ohio 
Canadian  Pacific 
Delaware  &  Hudson 

97% 
135% 

188 

1355/8 

188 

97% 
1341/4 
186 

971/4 
1341/4 
186 

=i| 

12,900 

Del.  Lak.  &  Western 

388% 

395 

385 

395 

+10  8 

1,200 

General  Klectric 

1811/4 

182 

181% 

181% 

+     % 

500 

Illinois  Central 

1501A 

150% 

149V8 

149% 

-1  % 

7,900 

Manhattan  Elevated 

169% 

169% 

1673/4 

167% 

+  1 

2,600 

New  York  Central 

136% 

13C>3/4 

135% 

136 

-  y* 

500 

N.Y.  N.H.  &H. 

201 

202 

2()13A 

202 

+2 

63,700 

Pennsylvania 

137V4 

137% 

136% 

18<5% 

—  % 

4,700 

Peoples  Gas 

109% 

lOS3^ 

1083/4 

+      V4 

85,700 

Heading 

75% 

77 

75l/£ 

753/8 

~~      ^ 

100 

Heading  pfd. 

88% 

88 

88% 

88 

—      1/4 

33,800 

Southern  Pacific 

6^% 

OS  3/s 

66% 

66% 

—1    % 

303,700 

Union  Pacific 

129% 

130V8 

127% 

128 

—      % 

Union  Pacific  pfd. 

97 

97 

971/4 

+      % 

43,100 

United  States  Steel 

27% 

28  2 

27 

27 

—          S/A 

72,800 

United  States  Steel  pfd. 

88 

88% 

871/4 

871/4 

—          % 

100 

Wells  Fargo  Express 

235 

235 

235 

235 

+4 

400 

Western  Union 

92 

923/8 

92 

92 

-     % 

In  the  first  column  is  shown  the  number  of  shares  of  stock  sold ;  in  the 
second,  the  name  of  the  stock ;  in  the  third,  fourth,  fifth,  and  sixth  respec- 
tively, the  opening,  highest,  lowest,  and  closing  prices  of  the  day ;  in  the 
last,  the  net  charges  between  the  closing  price  of  yesterday  and  to-day.  The 
plus  sign  signifies  an  advance  ;  the  minus  sign  a  decline.  Thus,  on  the  day 
given  123,500  shares  of  Amalgamated  Copper  stock  were  sold.  The  open- 
ing price  was  $81  per  share;  the  highest  price  for  the  day,  $81.75;  the 
lowest,  $79.62$;  the  closing,  $79.75,  which  shows  a  decline  of  $1.12}  from 
the  closing  price  of  the  preceding  day. 


STOCKS   AND   BONDS  395 


ORAL  EXERCISE 

1.  Find  in  the  table  (page  394)  three  cases  where  a  quotation 
both  for  common  stock  and  for  preferred  (pfd.  stands  for  pre- 
ferred) stock  is  given.     Which  is  worth  the  more  in  each  case  ? 
Under  what  circumstances  may  common  stock  sell   for  more 
than  preferred  stock  ? 

2.  What  would  100  shares  of  American  Sugar  Refinery  (com- 
mon) cost  if  bought  through  a  broker  at  the  lowest  price  for 
the  day,  brokerage  being  \% 


9 

3.    What  would  the  seller  of  the  stock  realize  on  the  sale  ? 


SUGGESTION.     The  seller  would  receive  the  price  for  which  it  was  sold 
minus  the  brokerage,  £  %. 

4.  State  the  cost,  at  the  opening  price  in  the  table,  of  100 
shares  of  each  of  the  following  stocks,  assuming  that  the  trans- 
actions take  place  through  a  broker  who  charges  \%  commis- 
sion :   Baltimore  &  Ohio ;   Canadian  Pacific ;   General  Electric  ; 
Manhattan  Elevated  ;  New  York  Central ;  Peoples  Gas ;  Wells, 
Fargo  Express;  New  York,  New  Haven  and  Hartford;  Illinois 
Central. 

5.  At  the  highest  price  in  the  table,  state  the  amount  re- 
ceived from  the  sale  of  100  shares  of  each  of  the  following 
stocks,   assuming  that  they  are  sold   through   a   broker  who 
charges  \°/0  commission :  Southern  Pacific  ;  United  States  Steel 
(preferred) ;  Western  Union  Telegraph  ;   Reading  (preferred) ; 
American  Sugar  Refinery  (common) ;   Pennsylvania  ;    Amalga- 
mated   Copper  ;   Union  Pacific  (preferred  ) ;  Adams  Express  ; 
Delaware,  Lacka wanna  and  Western  ;  New  York,  New  Haven, 
and  Hartford. 

WRITTEN   EXERCISE 

Find  the  cost,  at  the  dosing  price  in  the  table,  of  2500  shares 
of  the  folloiving   stocks,  including  brokerage : 

1.  Canadian  Pacific.  4.    Pennsylvania. 

2.  Amalgamated  Copper.  5.    Manhattan  Elevated. 

3.  American  Sugar  Refinery.        6.    United  States  Steel  (pref.). 


396  PRACTICAL   BUSINESS   ARITHMETIC 

At  the  closing  price  for  the  day  find  the  amount  received  from 
the  sale  of  3500  shares  of  the  following  stocks  sold  through  a  broker  : 

7.  Illinois  Central.  11.    Reading. 

8.  Western  Union.  12.    General  Electric. 

9.  Southern  Pacific.  13.    Canadian  Pacific. 

10.    Delaware  and  Hudson.  14.    Amalgamated  Copper. 

466.  Example.  I  bought  1000  shares  Pennsylvania  Railroad 
stock,  at  the  lowest  price  in  the  table,  and  sold  the  same  at 
140|.  Allowing  for  brokerage  both  for  buying  and  for  selling, 
did  I  gain  or  lose,  and  how  much  ? 

SOLUTION.     Since  I  bought  through  a   broker,  each   share  Iv.aiy 

cost  me  $  136.50  +  $  0.12$,  or  $  136.62J  ;  and  since  I  sold  through         136.  62| 
a  broker  the  proceeds  of  each  share  sold  was  $  140.50  —  $0.12$,         <jj  3.75 
or    $140.37$.     $  140.37$  -f  188.62$  =£$8.76,    gained  on    each 
share.    Since  $3.75  is  gained  on  1  share,  1000  times  $3.75,  or 


.  .  ,  ., 

$  3750,  is  gained  on  1000  shares. 

In  the  following  exercise  it  is  understood  that  all  sales  and  purchases  are 
made  through  a  broker  who  charges  a  commission  of  $  %  both  for  buying  and 
for  selling. 

WRITTEN  EXERCISE 

Find  the  gain  or  loss  on  oOO  shares  of  each  of  the  following 
stocks  bought  at  the  opening  price  and  sold  at  the  price  here  given: 

1.  Pennsylvania,  141|.  7.    Peoples  Gas,  97|. 

2.  Western  Union,  95.  8.    New  York  Central,  132. 

3.  Illinois  Central,  157.  9.    Baltimore  and  Ohio,  98|. 

4.  General  Electric,  195.  10.    Manhattan  Elevated,  170. 

5.  Canadian  Pacific,  131.  11.   Amalgamated  Copper,  84  j. 

6.  Southern  Pacific,  691.  12.   United  States  Steel  (pfd.),90|. 

13-24.  Find  the  gain  or  loss  on  1000  shares  of  each  of  the 
above  stocks  bought  at  the  lowest  price  and  sold  at  the  highest 
price  in  the  table. 

25.  F  bought  500  shares  of  Peoples  Gas  at  the  opening  price 
in  the  table  and  sold  it  so  as  to  gain  $750.  What  was  the  quoted 
price  when  he  sold  it  ? 


STOCKS   AND   BONDS  397 

26.  I  bought  some  Western  Union  Telegraph  stock  at  the 
opening  price  in  the  table  and  sold  it  for  94J.     If  by  so  doing 
I  gained  $  4500,  how  many  shares  did  I  buy  ? 

27.  I  bought  2500  shares  of  General  Electric  at  the  lowest 
price  in  the  table,  held  it  a  year,  received  5  %  in  dividends,  and 
then  sold  it  at  183|.     Did  I  gain  or  lose,  and  how  much,  money 
being  worth  4|  %  ? 

28.  I  gave  my  broker  orders  to  buy  1500  shares  Amalga- 
mated Copper  and  to  sell  2500  shares  Canadian  Pacific.      If  he 
buys  at  the  lowest  price  in  the  table  and  sells  at  the  highest 
price,  what  balance  will  he  put  to  my  credit? 

29.  At  the    closing  price  in  the   table,  find  the  total  cost 
of    500    shares    American    Sugar    Refinery    (preferred),    1500 
shares    General    Electric,    1000    shares   Manhattan    Elevated, 
100    shares    Peoples    Gas,    300   shares    Delaware   &    Hudson, 
and   500    shares    Illinois    Central. 

BONDS 

467.  A   negotiable   bond  is  a  very  formal   promissory  note 
issued  by  a  government,  railway,  or  industrial  corporation  for 
borrowed  money. 

Bonds  of  corporation  are  generally  issued  in  a  series  of  like  tenor  and 
amount,  and  bear  interest  payable  annually,  semiannually,  or  quarterly.  A 
bond  is  usually,  though  not  invariably,  issued  for  each  $  1000  borrowed. 

The  bonds  of  a  business  corporation  are  generally  secured  by  a  mortgage 
upon  its  property  (an  agreement  by  which  the  owners  of  the  bonds  may  sell 
the  property  if  the  bonds  and  interest  are  not  paid)  ;  but  the  bonds  of  a 
government  have  no  security  other  than  the  honor  of  the  people. 

The  bonds  of  a  business  corporation  with  reference  to  their  security  are 
of  various  kinds;  the  first-mortgage  bonds  usually  stand  highest,  in  that 
they  have  a  first  lien  on  the  property  covered  by  the  mortgage.  Second-  and 
third-mortgage  bonds  take  rank  after  the  first.  Debenture  bonds  are  unse- 
cured promises  to  pay ;  they  are  similar  in  principle  to  the  unsecured  paper 
of  a  merchant  offered  for  discount. 

468.  With  reference  to  the  form  of  contract  for  the  payment 
of  principal  and  interest  there  are  two  kinds  of  bonds  :  coupon 
and  registered. 


398 


PRACTICAL    BUSINESS   ARITHMETIC 


469.  A  coupon  bond  is  a  bond  to  which  are  attached  interest 
notes,  or  coupons,  representing  the  interest  due  on  the  bond  at 
stated  periods  of  payment. 


The  interest  notes  may  be  cut  off  from  the  bonds  at  maturity  and  the 
amount  of  interest  which  they  represent  collected  through  a  bank.  If  these 
notes  are  not  paid  when  due,  they  bear  interest  at  the  legal  rate. 


STOCKS   AND   BONDS  399 

470.  A  registered  bond  is  a  bond  which  has  no  separate  con- 
tract for  the  payment  of  the  interest.     Such  a  bond  must  be 
recorded  on  the  books  of  the  corporation  in  the  name  of  the 
holder  to  whom  the  interest  is  sent. 

Coupon  bonds  are  usually  drawn  payable  to  bearer  and  may  be  transferred 
by  delivery  or  indorsement,  or  both.  Registered  bonds  are  always  drawn 
payable  to  some  designated  person  and  can  be  transferred  only  by  assign- 
ment and  registry  on  the  books  of  the  corporation. 

471.  Bonds  issued  by  the  United  States  are  called  govern- 
ment bonds  or  government  securities ;  bonds  issued  by  a  state, 
state  bonds  or  state  securities  ;  bonds  issued  by  a  city,  municipal 
bonds  or  municipal  securities. 

The  names  of  the  different  government  bonds  are  usually  derived  from 
the  interest  they  bear  and  the  time  when  they  mature.  Thus,  "  U.  S.  2s, 
1930  "  are  United  States  bonds  bearing  interest  at  2%  and  maturing  in  1930 ; 
"  U.  S.  3s,  1908  "  are  United  States  bonds  bearing  3%  interest  and  maturing 
in  1908;  "  U.  S.  4s,  1925  "  are  United  States  bonds  bearing  4%  interest  and 
maturing  in  1925. 

472.  Bonds,  like  preferred  stock,  pay  a  fixed  income. 

From  the  gross  earnings  of  a  company  the  operating  expenses  are  first 
deducted;  from  the  net  earnings  are  deducted  all  fixed  charges,  such  as 
interest  on  bonds;  then  the  dividends  on  preferred  stock  are  paid;  and 
finally  out  of  the  remainder  dividends  on  the  common  stock  are  paid. 

ORAL  EXERCISE 

1.  Examine  the  bond  on  page  398.     With  reference  to  the 
form  of  contract,  what  kind  of  a  bond  is  it  ? 

2.  How  many  interest  notes  (coupons)   would  be  attached 
to  the  full  bond  ? 

3.  When  was  the  bond  issued  ?     What  date  (of  maturity) 
should  be  written  on  each  interest  note  ? 

4.  What  is  the  face  of  the  bond  ?     What   rate  of   interest 
does  it  bear  ?     What  sum  should  be  written  on  each  interest 
note? 

5.  How    may    coupon    bonds   be   transferred  ?      registered 
bonds  ? 


400 


PRACTICAL   BUSINESS   ARITHMETIC 


6.  If  the  bond  on  page  398  was  quoted  at  105|  when  it  was 
purchased,  how   much   did  it    cost,  including  \%   brokerage? 
How  much  did  the  seller  realize  on  it  ? 

7.  Has  the  city  or  town  in  which  you  live  any  bonded  in- 
debtedness (indebtedness  secured  by  bonds)  ?     If  so,  what  are 
these  bonds  called  and  what  rate  of  interest  do  they  pay  ? 

BUYING  AND  SELLING  BONDS 

473.  Bonds,    like    stocks,    are    usually    bought    and    sold 
through  brokers. 

The  broker's  commission  for  buying  and  selling  bonds  is  the  same  as  for 
buying  and  selling  stocks. 

474.  The  following   table   is   an   abbreviated   form    of   the 
sales,  and  opening,  highest,  lowest,  and  closing  prices  of  bonds 
traded  in  on  the  New  York  Exchange  on  a  recent  date. 

TABLE  or  SALES  AND  RANGE  OF  PRICES 


SALES 

BONDS 

OPEN. 

HIGH. 

Low. 

CLOS. 

$  8000 

Am    Hide  &  Leather  6s  

97  ¥9 

97% 

97% 

97% 

241  000 

Brooklyn  Rapid  Transit  4s          .    . 

89?£ 

89  i/o 

89 

891A 

1,000 
571,000 
10,000 
71,000 
2,000 
12,000 
19  000 

Chesapeake  &  Ohio  6s,  1911  
Chicago,  Burlington  &  (Juincy  4s  . 
Denver  &  Rio  Grande  4s  .  .  .  .  
Erie  4s  
Illinois  Central  4s,  1952    
Lac  ka  wanna  Steel  5s   
Missouri  Pacific  4s 

110 

1011/2 

100% 

IDS 
108 

1063/8 

95 

110 
101% 
100% 
108V8 
IDS 

10(534 

'16 

110 

1013/g 

99% 
107% 
107% 
106% 
95 

110 
101% 
99% 
1073/4 
108 
,063/4 

1,000 
16,000 
5000 

National  Starch  6s   
Northern  Pacific  1st  mtg.  4s  
Pennsylvania  4%s  

85 

105% 
lOhS/. 

85 
106l/8 
109 

85 
108% 

85 
105% 
109 

11  000 

Seaboard  Air  Line  4s    ... 

COT/ 

90 

891/8 

89  s/a 

17,000 

Seaboard  Air  Line  5s   

103% 

104% 

104 

101  8 

87,000 
1,000 
5,000 

Union  Pacific  1st  mtg.  4s  
United  States  reg.  4s.,  1907  
United  States  coupon  4s  

l053/4 
104V2 
104V4 

105% 
104% 

105% 
104# 

104 

105% 
104% 
104i/4 

In  the  first  column  is  shown  the  par  value  of  the  bonds  sold ;  in  the  sec- 
ond, the  name  of  the  bonds  and  the  interest  they  bear ;  in  the  third,  fourth, 
fifth,  and  sixth,  respectively,  the  opening,  highest,  lowest,  and  closing  prices 
of  the  day.  These  prices  are  quoted  at  a  rate  per  $  100  of  par  value  (amount 
of  the  bond).  Thus,  on  the  day  given  $  241,000  worth  of  Brooklyn  Rapid 
Transit  bonds  bearing  4%  interest  were  sold.  The  opening  price  was 
I  89.25  per  $  100  of  par  value,  the  highest  price,  $  89.50,  the  lowest  price,  $  89, 
and  the  closing  price,  $  89.25  per  $  100  of  par  value. 


STOCKS   AND   BONDS  401 

475.  Example.  What  is  the  cost  of  150,000  (par  value) 
Chicago,  Burlington  &  Quincy  4  %  bonds  at  the  highest  price 
quoted  in  the  table  (page  400)  ? 

SOLUTION.     $100  of  par  value  cost  $101|  +  $0.12|  brokerage,  or  $  102. 

.  •.  $  50,000  of  par  value  will  cost  500  times  ($  50,000  -=-  $  100)  $  102,  or  $  51,000. 

WRITTEN  EXERCISE 

1.  What  is  the  cost  of  $ 25,000  American  Hide  and  Leather 
bonds  at  the  opening  price  in  the  table  ? 

2.  I  gave  my  broker  orders  to  sell  $10,000  Chesapeake  and 
Ohio  6  %  bonds  and  buy  $  10,000  National  Starch  6  %  bonds. 
If  he  sold  at  the  highest  price  in  the  table  and  bought  at  the 
lowest  price,  what  balance  should  he  place  to  my  credit  ? 

3.  Find   the   proceeds   from    the    following    sales  :    $  1000 
United  States  4  %  registered  bonds  at  the  opening  price  in  the 
table  ;  $  5000  United  States  4  %  coupon  bonds  at  the  opening 
price  in   the   table  ;    $  75,000  Chicago,  Burlington  &  Quincy 
4%  bonds  at  the  closing  price  in  the  table  ;  $10,000  Erie  4% 
bonds  at  the  lowest  price  in  the  table. 

4.  June  1, 1907,  a  certain  city  borrowed  $  250,000  with  which 
to  build  a  new  high  school,  and  issued  4|%    10-yr.  coupon 
bonds  as  security.     If  these  bonds  sold  (through  a  broker)  at 
101 J,  how  much  was  received  by  the  city  ?     If  A  bought  five 
$  1000  bonds,  how  much    did  they  cost   him  ?     If  interest  is 
payable  semiannually,  what  date  (of  maturity)  should  the  last 
interest  note  of  each  bond  bear  ?     What  will  be  the  amount  of 
each  interest  note  ? 

5.  Find  the  total  cost  of  the  following  purchases  :   $  20,000 
Erie  4%  bonds  at  the  closing  price  in  the  table  ;  $  2000  Illinois 
Central  4  %   bonds  at  the  lowest  price  in  the   table  ;  $  5000 
Lackawanna  Steel  5  %  bonds  at  the  lowest  price  in  the  table ; 
$  15,000  Missouri  Pacific  4  %  bonds  at  the  opening  price  in  the 
table  ;    1 10,000  Northern  Pacific  first-mortgage  4  %  bonds  at 
the  lowest  price  in  the  table  ;  $  3000  Pennsylvania  4  J  %  bonds 
at  the  opening  price  in  the  table. 


402  PRACTICAL   BUSINESS   ARITHMETIC 

INCOMES  AND   INVESTMENTS 

ORAL   EXERCISE 

1.  A  bought  a  4  %  United  States  bond  at  H9J.     Not  con- 
sidering the  question  of  the  maturity  of  the  bond,  what  rate  of 
income  did  he  receive  on  his  investment  ? 

SUGGESTION.    $  4  is  what  per  cent  of  $  120  ? 

2.  B    bought   4  %   bonds   having   a    market    value    of    79J. 
What  rate  per  cent  of  interest  did  he  receive  011  his  invest- 
ment ? 

3.  C  bought  110,000   worth  of  6%  bonds  quoted  at  149|, 
and  $10,000  4|%  bonds  quoted  at  112|.     What  rate  of  income 
did  he  receive  from  both  investments  ? 

4.  D  bought  a  Seaboard  Air  Line  4  %  bond  at  the  opening 
price  in  the 'table,  also  a  Seaboard  Air  Line  5%  bond  at  the 
opening  price  in  the  table.     Interest  being  payable  annually 
in  each  case,  which  will  yield  the  larger  income  ? 

The  rates  of  interest  paid  on  bonds  of  high  class  security  are  very 
much  lower  at  the  present  time  than  they  were  a  generation  ago.  For 
example,  in  1865  the  National  Government  paid  over  7%  interest  on  30% 
of  its  debt,  6%  on  10%  of  its  debt,  5%  on  55%  of  its  debt,  and  4%  on  5% 
of  its  debt.  At  the  present  time  about  one  half  of  the  United  States  bonds 
pay  only  2%  interest;  and  the  average  rate  of  interest  paid  on  railroad 
bonds  is  about  4%. 

476.  As  a  general  rule,  a  bond  of  undoubted  security  which 
bears  a  high  rate  of  interest  commands  so  large  a  premium  as 
to  reduce  the  actual  return  on  the  investment  to  the  prevailing 
rates  on  other  investments  of  as  good  security.     (See  problem 
4  in  the  foregoing  exercise.) 

477.  At  the  maturity  of  a  bond  only  its  face  value  and  the 
interest  accrued  thereon  are  paid  to  the  holder.     In  order  to 
command  a  high  price,  therefore,  a  bond  must  pay  a  good  rate 
of  interest,  be  perfectly  safe,  and  have  a  long  period  to  run. 

Thus,  a  6  %  third-mortgage  bond  having  10  yr.  to  run,  or  a  6%  first- 
mortgage  bond  having  only  2  yr.  to  run,  might  not  command  as  high  a  price 
as  a  3  %  bond  having  a  high  class  security  and  30  yr.  to  run. 


STOCKS   AND   BONDS  403 

WRITTEN  EXERCISE 

1.  A  bought  a  5%   bond  quoted  at   149|.     What   rate  of 
interest  did  he  receive  on  the  money  invested  ? 

In  the  above  and  all  similar  problems  the  question  of  the  maturity  of  the 
bond  is  not  considered,  and  it  is  assumed  that  the  transaction  was  effected 
through  a  broker  who  charged  a  commission  of  1%. 

2.  F  invested  §42,600  in  Lackawanna  Steel  5%    bonds  at 
the  opening  price  in  the  table  (page  400).     What  was  his  an- 
nual income  ? 

3.  Which  gives  the  better   income  and    how  much,  a  5% 
bond  bought  at  79J  or  a  6  %  bond  bought  at  119f  ?    6  %  stock 
bought  at  149J  or  4£  %  stock  bought  at  112f  ? 

4.  G    invested    $24,312.50    in    Adams    Express   Company 
stock  at  the  closing  price  in  the  table   on  page  394.     What 
was  his  annual  income  from  a  3|  %  quarterly  dividend  ? 

5.  H  invested  $  79,025  in  Delaware,  Lackawanna  &  West- 
ern Railroad  stock  at  the  closing  price  in  the  table,  page  394. 
What  will  be  his  annual  income  when  the  dividends  are  4^% 
quarterly  ? 

6.  Which  would  be  the  more  profitable  as  an  investment, 
to  buy  Missouri  Pacific  first-mortgage  4%  bonds,  due  in  1925, 
at  95|-,  or  Edison  Electric  Co.  first-mortgage  5  %  bonds,  due  in 
1925,  at  104$  %  ? 

7.  When  the    current  rate  of  interest  is  4J%,  what  price 
can  I  afford  to  pay  for  Chesapeake  and  Ohio  6  %  first-mortgage 
bonds  ?     (Give  the  nearest  J  in  your  answer.) 

8.  What   sum   must   be    invested  in   Illinois    Central    4  % 
bonds,  at  the  opening  price  in  the  table,  page  400,  to  realize  an 
annual  income  of  I  2000  ? 

SOLUTION.     $4  =  the  income  on  $  100  of  the  par  value  of  the  bonds. 
$2000  -$4  =  500. 

.-.  bonds  having  a  par  value  of  500  x  $  100  must  be  purchased. 
But  the  cost  is  $  108  +  $  0.121  Or  $  108. 12|. 
.-.  500  x  $108.12i  or  $54062.50  must  be  invested. 


404 


PRACTICAL   BUSINESS   ARITHMETIC 


9.  What  sum  must  be  invested  in  Missouri  Pacific  4  % 
bonds  at  the  closing  price  in  the  table,  page  400,  to  realize  an 
annual  income  of  $  1500  ? 

10.  Using  the  closing  price  (with  brokerage)  in  the 
tables  on  pages  394  and  400,  find  which  gives  the  better  in- 
come and  how  much  :  Illinois  Central  Railroad  stock  paying 
6  %  dividends  or  Denver  &  Rio  Grande  4  %  bonds  ;  General 
Electric  stock  paying  8  %  dividends  or  Lacka wanna  Steel  5  % 
bonds  ;  New  York,  New  Haven  &  Hartford  Railroad  stock  pay- 
ing 8  %  dividends  or  United  States  4  %  coupon  bonds  ;  Man- 
hattan Elevated  Railroad  stock  paying  6|  %  dividends  or  Erie 
4  %  bonds. 

STOCK   EXCHANGES 

478.  Stock  exchanges  are  associations  organized  for  the  pur- 
pose of  creating  a  regulated  market  for  the  buying  and  selling 
of  stocks  and  bonds.  The  principal  stock  market  of  the  United 
States  is  the  New  York  Stock  Exchange,  an  unincorporated 
association  of  1100  members. 

There  are  stock  exchanges  in  Chicago,  Philadelphia,  Boston,  and  other 

large  cities,  but  these  are  local 
institutions  and  their  dealings 
are  confined  to  local  stocks. 
The  New  York  Stock  Exchange 
is  a  national  institution  which 
deals  with  the  securities  of  the 
wrhole  nation. 

A  membership  in  a  stock  ex- 
change is  called  a  "seat."  The 
price  of  a  seat  varies  from 
$10,000  to  $20,000  on  local 
stock  exchanges,  to  from 
$30,000  to  $75,000  on  the  New 
INTERIOR  OF  A  STOCK  EXCHANGE.  York  stock  Exchange.  A  stock 

exchange    always   maintains   a 

uniform  rate  of  commission.  This,  as  has  been  seen,  is  usually  |%,  or  $  12.50 
per  100  shares ;  but  as  every  purchase  by  a  broker  is  usually  followed  by  a 
sale,  the  commission  on  one  transaction  both  ways  amounts  to  £%,  or  $25 
per  100  shares. 


STOCKS   AND   BONDS 


405 


479.  The  principal  ways  in  which  stocks  are  bought  and  sold 

are  as  follows :  "  cash,"  that  is,  deliverable  on  the  day  of  sale ; 
" regular"  that  is,  deliverable  on  the  day  following  the  sale  ; 
"at  three  days"  that  is,  deliverable  on  the  third  day  of  the  sale; 
"  buyer's  option"  that  is,  deliverable  at  the  option  of  the  buyer 
at  any  time  within  the  option  period  (from  4  to  60  days)  ; 
"  seller  s  option"  that  is,  deliverable  at  the  option  of  the  seller 
any  time  within  the  option  period. 

By  far  the  largest  part  of  the  sales  are  "  regular."  On  "  cash,"  "  regular," 
and  "  at  three  days "  sales  no  interest  is  paid ;  but  on  options  over  three 
days,  interest  at  the  legal  rate  on  the  selling  price  of  the  stock  is  paid  by 
the  buyer  to  the  seller.  To  terminate  an  option  of  over  three  days,  one 
day's  notice  is  required. 

480.  A  margin  is  a  sum  of  money  deposited  with  a  broker  to 
cover  losses  which  he  may  sustain  on  behalf  of  his  principal. 

Stocks  and  bonds  are  frequently  bought  and  sold  on  a  margin.  The 
process  may  be  illustrated  in  the  following : 

June  8,  A.  M.  Greyson  deposited  with  Richard  Roe  &  Co.,  his  brokers, 
$  4160,  and  instructed  them  to  buy  400  shares  of  Atchison,  Topeka  and  Santa 
Fe  Railroad  stock  whenever  they  could  do  so  at  104.  On  the  same  day  the 
stock  was  bought  in  accordance  with  instructions.  On  June  14,  pursuant 
to  instructions,  Richard  Roe  &  Co.  sold  the  stock  at  107£  and  sent  A.  M. 
Greyson  the  following  statement  and  a  check  for  $5322.56. 


New  York,. 


In  account  current  with   RICHARD  ROE   &   CO. 


jk*"* 


7^-cA^c^A^U^i^. 


J7 
.yj  2.2- 


DAYS    INTEREST 


37 


(,0 


By  the  above  transactions  A.  M.  Greyson  has  gained  $1162.56. 

The  amount  of  margins  demanded  by  a  broker  depends  upon  the  charac- 
ter of  the  stocks  traded  in.  On  stocks  that  have  a  good  market  10%  of  the 
market  value  is  usually  demanded ;  on  stocks  that  have  little  or  no  market 


406  PEACTICAL   BUSINESS   ARITHMETIC 

20  %  of  the  market  value  or  more  is  often  required.  The  broker,  of  course, 
pays  for  the  stock  in  full.  In  order  to  do  this  he  is  frequently  obliged  to 
borrow  money  from  a  bank.  This  he  may  usually  do  by  depositing 
(hypothecating)  stock  as  security  (see  page  328). 

The  speculators  on  the  stock  exchange  may  be  divided  into  two  classes  : 
bulls  and  bears.  A  bull  is  a  speculator  who  buys  stocks  in  the  expectation 
of  selling  them  at  a  higher  price.  A  bear,  is  a  speculator  who  sells  stocks 
which  he  does  not  own,  in  the  expectation  that  he  can  buy  them  at  a  lower 
price  before  the  date  on  which  they  must  be  delivered.  A  bull  who  has 
bought  is  said  to  be  "long"  of  stock;  a  bear  who  has  sold  is  said  to  have 
sold  short,"  or  to  be  "short"  of  stock.  A  bull  works  for  advancing  prices; 
a  bear  for  declining  prices.  A  bull,  when  he  sells  at  higher  prices,  is  said 
to  have  "realized"  his  profits;  when  at  lower  prices,  to  have  "liquidated." 
A  bear,  when  he  buys  stock,  is  said  to  have  "covered"  no  matter  whether  he 
bought  at  a  gain  or  at  a  loss. 

WRITTEN  EXERCISE 

1.  On  June  25  I  purchased  through  a  broker  300  shares  of 
Amalgamated  Copper  at  87J  b.   3  (buyer's   option  any    time 
within  3  da.).     On  June  28  the  stock  was  delivered  and,  pur- 
suant to  my  instructions,  sold  for  89 J  cash.     Did  I  gain  or  lose, 
and  how  much  ? 

2.  On  Apr.    15    my  broker  purchased  for  me   500   shares 
Delaware  &  Hudson  at  172|  regular.     On  April  16  he  sold  the 
same  at  174^  cash.     What  was  my  gain? 

3.  On   Sept.    15  I  bought,    through   a   broker,    250   shares 
Reading  pfd.  at  68|  b.  30.     On  Sept.  25  my  broker  demanded 
the  stock  and,  in  accordance  with  my  instructions,  sold  it  for 
70 \  regular.     Did  I  gain  or  lose,  and  how  much? 

4.  On  Dec.  1  D  bought  of  me  through  C,  his  broker,  2000 
shares  of  Missouri  Pacific  at  99 \  s.  60  (seller's  option  any  time 
within  60  da.).     Dec.  17  C,  pursuant  to  my  instructions,  de- 
livered  the   stock   which   he  had   purchased   for   me   on   the 
previous  day  at  96  regular.     Did  I  gain  or  lose,  and  how  much? 

5.  On  June  27  I  ordered  my  broker  to  sell  "short"  for  me 
500  shares  Baltimore  &  Ohio  at  105J  s.  30.     July  7  the  stock 
declined  to  100J.     I  ordered  my  broker,  at  this  price,  to  "cover 
my  short."     Did  I  gain  or  lose,  and  how  much  ? 


STOCKS   AND   BONDS 


407 


6.  Jan.  15  I  deposited  $4080  with  my  broker  and  instructed 
him  to  buy  400  shares  of  Baltimore  &  Ohio  whenever  he  could 
do  so  at  102  regular.     On  the  same  day  he  bought  the  stock  as 
directed.     On  Feb.  27  I  ordered  him  to  sell,  and  he  did  so  at 
105|  cash.     What  was  my  net  gain? 

7.  May  25  a  speculator  sent  his  broker  a  margin  of  $  2000 
with  which  to  buy  100  shares  Metropolitan  Street  Railway  at 
165    regular.     The  broker  invested  as  directed.     On  May  27 
the  stock  rose  to  170|  and  the  broker  was  authorized  to  sell. 
If  he  sold  regular  at  this  price,  what  was  the  speculator's  gain  ? 
the  broker's  commission? 

8.  What  is  the  balance  due  on  the  following  account  current : 


M 


New  York,. 


In  account  current  with  RICHARD  ROE  &  CO. 


DAYS    INTEREST 


PRODUCE  EXCHANGES 

481.  Just  as  there  are  stock  exchanges  in  many  of  the  large 
cities  to  supply  a  regular  market  for  the  purchase  and  sale  of 
securities,  so  there  are  produce  exchanges  (also  called  boards  of 
trade,  chambers  of  commerce,  etc.)  to  supply  a  regulated  market 
for  the  purchase  and  sale  of  farm  crops. 

Produce  exchanges  are  important  accessories  of  commerce.  They 
promote  just  and  equitable  principles  of  trade ;  establish  and  maintain  a 
uniformity  in  commercial  usages ;  and  acquire,  preserve,  and  disseminate 
valuable  business  information.  The  more  important  produce  exchanges, 
by  inspecting  and  grading  all  of  the  important  food  products,  protect  the 
public  against  fraud  and  adulterations.  The  cereals,  for  example,  are 


408 


PRACTICAL   BUSINESS   ARITHMETIC 


inspected  and  graded  according  to  their  quality.  There  are  usually  four 
grades  of  wheat  and  corn,  five  of  barley,  and  three  of  oats  and  rye;  No.  i 
wheat  is  the  best  quality;  No.  4,  the  poorest;  etc. 

The  principal  produce  exchange  in  the  United  States  is  the  Chicago  Board 
of  Trade.  On  the  floors  of  this  exchange  are  bought  and  sold  a  large  part 
of  the  cereals  and  the  meat  products  of  the  Mississippi  Valley  and  the 
West.  The  association  thus  practically  determines  the  price  of  these  com- 
modities, not  only  for  the  United  States,  but  for  the  world. 

Commodities  are  bought  and  sold  on  the  exchanges  for  present  or  for 
future  delivery.  Contracts  for  present  delivery  are  called  "  cash  "  contracts  ; 
contracts  for  future  delivery,  "  futures."  Speculative  trading  in  grain  and 
cotton  is  usually  in  "futures." 

The  established  brokers'  commissions  for  transactions  on  the  Chicago 
Board  of  Trade  are  as  follows :  for  grain,  \<f>  per  bushel;  for  pork,  2|^  per 
barrel ;  for  lard  and  ribs,  2|  $  per  100  Ib. 

The  lowest  margins  received  are:  on  grain,  $20  per  1000  bu.;  on  pork, 
$125  per  250  bbl. ;  on  lard,  $  175  per  250  tierces ;  on  ribs,  $125  per  50,000  Ib. 
Of  course  the  margins  demanded  are  sometimes  considerably  higher  than 
the  above  figures. 


OPEN.    HIGH.  Low.  CLOSE. 


Wheat  —  July 

Sept. 

Dec. 
Corn  —  July 

Sept. 

Dec. 
Oats  — July   .. 

Sept.  .. 
Pork  — Sept.  .. 

Oct.  . . . 
Lard  — Sept.  .. 

Oct.  . . . 
Eibs  — Sept.  .. 

Oct. 


..87 
..87 


89% 


In  the  accompanying  table  is 
shown  the  opening,  highest,  lowest, 
and  closing  prices  of  provisions  for 
a  certain  day  on  the  Chicago  Board 
of  Trade. 

"Wheat — July"  signifies  wheat 
to  be  delivered  in  July  ;  "  Wheat  — 
Sept."  wheat  to  be  delivered  in  Sep- 
tember; etc.  The  usual  time  for  fu- 
ture delivery  is  during  the  months  of  May,  July,  September,  and  December. 

In  the  following  exercise  it  is  assumed  that  all  transactions  are  effected 
through  a  broker  who  charges  the  usual  commission. 

WRITTEN  EXERCISE 

1.  What  will  it  cost  me  to  buy  5000  bu.   September  wheat 
at  the  opening  price  in  the  table  ? 

2.  C  bought  6000  bu.  July  oats  at  27^  per  bushel  and  sold 
the  same  at  the  closing  price  in  the  table.     What  was  his  net 
gain  ? 

3.  B  bought  15,000  bu.   July  corn  at  the  lowest  price  and 
sold  the  same  at  the  highest  price  in  the  table.     Did  he  gain 
or  lose,  and  how  much  ?     What  per  cent  ? 


STOCKS   AND  BONDS  409 

4.  G  bought  2250  tierces  (765,000  Ib.)  of  October  lard  at 
$  7.26-J  and  sold  the  same  at  the  closing  price  in  the  table.     Did 
he  gain  or  lose,  and  how  much  ? 

5.  F  bought  1500  bbl.   of  September  pork  at  the  opening 
price  and  sold  the  same  at  the  closing  price  in  the  table.     Did 
he  gain  or  lose,  and  how  much  ? 

6.  D  ordered  his  broker  to  sell  5000  bu.  September  corn  and 
buy   5000   bu.    December   corn.     If   the   broker    sold    at   the 
highest  price  and  bought  at  the  lowest  price  in  the  table,  what 
amount  should  he  remit  D  ? 

7.  A  broker  bought  on  his  own  account  10,000  bu.  of  each, 
September  wheat,  December  corn,  and  July  oats,  at  the  opening 
price,  and  sold  the  same  at  the  closing  price  in  the  table.     Did 
he  gain  or  lose,  and  how  much  ? 

8.  H  sold  " short"   10,000    bu.    September   wheat  at  the 
highest   price   in   the  table.       September  wheat  subsequently 
declined   to    85 J   and  he  bought  at  this  price  to  "cover  his 
short."     Did  he  gain  or  lose,  and  how  much  ? 

9.  June  27  I  deposited  with  my  broker  a  margin  of  $  200  for 
the  purchase  of  5000    bu.  of  September  wheat  at  the  lowest 
price  in   the   table.     On  July  25  I  ordered  him  to  sell.     He 
did  so,  receiving  89f  ^  per  bushel.     How  much  should  he  pay 
me  in  settlement  ? 

10.  Aug.  5  I  deposited  with  my  broker  $2500  as  a  margin  for 
the  purchase  of  5000  bbl.  of  October  pork  at  the  closing  price 
in  the  table.  On  Sept.  2  I  ordered  him  to  sell  at  113.071. 
He  did  so  and  remitted  me  a  check  for  the  amount  due. 
What  was  the  amount  of  the  check  ? 


CHAPTER   XXXIV 

LIFE   INSURANCE 

482.  Life  insurance  companies,  like  fire  insurance  companies 
(page  274),  are  usually  either  stock  companies  or  mutual  com- 
panies. 

There  are  also  assessment  companies  and  fraternal  beneficiary  associa- 
tions. These  usually  depend  upon  monthly  assessments  or  "calls"  to  pay 
death  claims.  They  are  required  by  law  to  hold  but  comparatively  little, 
if  anything,  as  a  fund  from  which  to  pay  losses. 

483.  Insurance  rates  are  always  a  certain  price  per  $  1000  of 
insurance.       They   are    payable     annually,    semiannually,    or 
quarterly  in  advance. 

484.  The  four  leading  kinds  of  policies  are :    ordinary  life, 
limited  life,  endowment,  and  term. 

485.  An  ordinary  life  policy,  in  consideration  of  premiums  to 
be  paid  during  the  life  of  the  insured,  guarantees  to  pay  at  his 
death  a  stated  sum  of  money. 

486.  A  limited  life  policy,  in  consideration  of  premiums  to 
be  paid  for  a  fixed  number  of  years,  guarantees  to  pay  a  stated 
sum  of  money  at  the  death  of  the  insured. 

It  will  be  observed  that  in  an  ordinary  life  policy  the  premiums  are  pay- 
able during  the  life  of  the  insured,  while  in  a  limited  life  policy  they  are 
payable  for  a  fixed  number  of  years,  when  the  policy  becomes  paid  up  (no 
more  premiums  due).  The  premium  is  higher  on  the  latter  form  of  policy. 

487.  An    endowment   policy,  in   consideration  of    premiums 
paid  for  a  fixed  number  of  years,  guarantees  to  pay  a  stated 
sum  of  money  to  the  insured  at  a  certain  time  or  to  the  bene- 
ficiary (one  in  whose  favor  the  insurance  is  effected)  in  case  of 
prior  death. 

488.  A  term  policy,  in  consideration  of  premiums  paid  for  a 
fixed  time,   guarantees  to  pay  a  stated  sum  of   money  if  the 
insured  dies  within  the  term  of  insurance. 

410 


LIFE   INSURANCE 


411 


Thus,  a  person  may  insure  his  life  for  a  limited  number  of  years  only. 
Since  the  company  may  never  be  called  upon  to  pay  the  insurance,  the 
premiums  on  these  policies  are  low. 

489.  The  reserve  is  that  part  of  the  premiums  of  a  policy, 
with  interest  thereon,  required  by  law  to  be  set  aside  as  a  fund 
to  be  used  in  payment  of  the  policy  when  it  falls  due. 

The  legal  rate  of  interest  on  reserve  .funds  varies  slightly  in  different 
states.  The  higher  the  rate  of  interest,  the  smaller  the  reserve  required. 

490.  The  surplus  of  an  insurance  company  is  the  excess  of 
its  assets  (resources)  over  its  liabilities. 

This  fund,  with  certain  restrictions,  may  be  used  for  such  purposes  as 
the  company  deems  best.  After  retaining  a  surplus  large  enough  to  pro- 
vide for  contingencies,  companies  which  issue  policies  on  the  mutual  or 
participating  plan  divide  the  remainder  of  the  surplus  among  such  of  its 
policy  holders  as  are  entitled  to  share  in  it.  This  is  practically  a  return  of 
an  overcharge,  but  it  is  usually  called  the  payment  of  a  dividend. 

491.  Dividends  may  be  used:   (1)  to  reduce  the  next  year's 
premium  ;   (2)  to  purchase  additional  insurance,  payable  when 
the  policy  matures ;   (3)  to  shorten  the  time  to  run. 

Dividends  may  also  be  left  with  the  company,  with  the  distinct  under- 
standing that  there  shall  be  no  division  of  the  same  until  the  end  of 
a  certain  period.  As  the  policyholder  receives  no  benefit  unless  he 
survives  the  selected  period,  it  will  be  seen  that  the  return  should  be  some- 
what larger.  This  plan  is  called  semi-tontine,  distribution  period,  accumu- 
lated surplus,  deferred  dividend,  etc. 

492.  If  a  policy  is  discontinued,  the  insured  may  secure  an 
equitable  return  for  the  reserve  accumulated. 

The  insured  usually  has  several  options  in  this  matter  :  (1)  he  may  take 
the  cash  value,  or  practically  all  of  the  reserve  value  of  the  policy ;  (2)  he 
may  take  a  paid-up  policy  for  such  an  amount  as  its  reserve  value  will  pur- 
chase ;  (3)  he  may  take  extended  insurance  for  the  face  of  the  policy  for  as 
many  years  and  days  as  its  reserve  value  will  purchase. 

ANNUAL  PREMIUM  RATES  FOR  AN  INSURANCE  OF  $1000 


AGE 

OIMMNAIIY 
Lira 

20-  PAYMENT 

LIFE 

15-YKAR 

ENDOWMENT 

20-YEAR 

ENDOWMENT 

25 

20.93 

30.90 

66.57 

48.93 

30 

23.75 

33.76 

67.27 

49.72 

35 

27.39 

37.25 

68.26 

50.88 

40 

32.  16 

41.60 

69.  76 

52.70 

50 

47.23 

54.65 

76.20 

60.59 

412  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  What  kind  of  a  policy  is  that  011  page  413  ?     Who  is  the 
beneficiary?   the   insured?      What   is    the   annual   premium? 

2.  Should  the  beneficiary  die  in  1912,  to  whom  would  the 
policy  be  payable  at  the  death  of  the  insured  in  1920  ? 

3.  Should  the  insured   die  after  having  paid  one  annual 
premium,  how  much  would  his  heirs  receive  ? 

4.  If  the  surplus  earnings  (dividends)  on  the  policy  amount 
to  $  1200,  at  the  end  of  10  yr.,  how  much  cash  (see  page  414) 
would  the  insured  receive  should  he  surrender  the  policy  ? 

5.  Should  the  insured  decide  to  discontinue  paying  premiums 
after  making  five   annual  payments,    how   much   ptaid-up   in- 
surance, exclusive  of  the  surplus,  might  he  receive  ? 

6.  How  large  a  sum  may  the  insured  borrow  on  the  policy 
after  ten  premiums  have  been  paid  ? 

7.  If  the  company  secures  interest  in  advance  by  deducting 
it  from  the  amount  of  the  loan,  and  the  insured  should  borrow 
$4000  for  one  year  at  5  %,  what  would  be  the  amount  of  the 
check  which  he  would  receive  from  the  company  ? 

8.  Had   the   insured    taken    out   the   policy  when  he  was 
twenty-five  years  of  age,  what  would  be  the    annual   saving, 
exclusive  of  interest,  in  the  cost  ?     How  much  would  he  have 
saved  in  15  yr.  ?  in  20  yr.  ? 

9.  If  the  insured  should  discontinue  paying  premiums  after 
5  yr.    and   take    extended   insurance,    how   much    would    the 
beneficiary  receive  should  the  insured  die  in  1914?  in  1919? 

10.  If  the  insured  had  taken  a  life  policy  (see  rates,  page 
411)  for  the  same  amount,  instead  of  an  endowment  policy,  and 
died  after  having  paid  ten  full  premiums,  how  much  less  would 
his  insurance  have  cost,  exclusive  of  dividends  and  interest  ? 

11.  If  the  insured  should  pay  four   full   premiums   on   the 
policy,  take  extended  insurance,  and  die  5  yr.  later,  how  much 
would  his  beneficiary  receive  ? 

12.  If  the  insured  discontinues  making  payments  after  seven 
annual  premiums  had  been  paid,  how  much  would  he  get  in 
cash  at  the  end  of  20  yr.  from  date  of  issue,  if  living  ? 


LIFE   INSURANCE 


413 


AGE 


SUM  INSURED 
$/  '0,000 
YEARLY  PREMIUM 


I  n  Consideration  of  the  Application  for  this  Policy,  hereby  made  a  part  of  this  contracf, 

The  Penn  Mutual  Life  Insurance  Company  of  Philadelphia 

insures  thejife  of WWWtQ   ^.(£dfcm?OU   ~ r~^ 

in  the  County  of      ff  VOttfOl  State  of 


• — ~ — -  Dollars,  and  promises 
to  pay  at  its  Home  Office,  in  the  City  of  Philadelphia,  unto    ' ' — — " 

executors,  administrators,  or  assigns,  the  said  sum  insured  on  the 
day  of  <^P&&&/     in  the  year  nineteen  hundred  and--^^ 
or  if  the  said  insured  should  die^before  that  time  then  to  make  said  payment  to 

<T«S  ..      *  .  ^*  ,<•*-*    0>  .  L.  .  f:  .,.?..  ./)        /)  /?• 


ENDOWMENT 

IN    2-0    YEARS 
Regular 


executors,  administrators,  or  assigns,  upon  receipt  of  satisfactory  proof  of  the  death  of  the 
insured,  during  the  continuance  in  force  of  this  Policy,  upon  the  following  conditions,  namely  : 
payment  in  advance  to  the  Company,  at  its  Home  Office,  of  the  sum  of 

•£  ^y/oo  —  Dollars,  at  the  date  hereof,  and  of  the 
premium  of  ^^e.J^J«^^^<^fe^^C^%:x^»Dollars, 
at  or  before  three  o'clock  P.M.,  on  the     ^e^t^n^  day  of    v-/^^2^x 

in  every  year  during  the  continuance  of  this  contract,  or  until 


%tt/&?z6y  full  years'  premiums  shall  have  been  paid : 


This  Policy  shall  participate  annually  in  the  surplus  earnings  of  the  Company  in  accord- 
ance with  the  regulations  adopted  by  the  Board  of  Trustees. 

The  extended  insurance*  paid-up  insurance,  and  loan  or  cash  surrender  value  privileges, 
benefits,  and  conditions  stated  on  the  second  page  hereof  form  a  part  of  this  contract  as  fully 
as  if  recited  at  length  over  the  signatures  hereto  affixed. 

In  Witness  Whereof,  The  Penn  Mutual  Life  Insurance  Company 

of  Philadelphia  has  caused  this  Policy  to  be  signed  by  its  President,  Secretary,  and 
Actuary,  attested  by  its  Registrar,  at  its  Home  Office,  in  Philadelphia,  Pennsylvania,  the 
day  of         <_x^<£^//  19  07, 


Secretary. 


/    J 


Attest 


President. 


Actuary. 


414 


PRACTICAL   BUSINESS   ARITHMETIC 


Table  of  Extension,  Paid-up,  and  Loan  or  Cash  Values,  provided 
for  by  the  Policy,  if  no  indebtedness  exists  against  it 


AT 
END  OF 
YEAR 

TERM  OF  EXTENSION 
FOR  THIS  POLICY 

These  Values  are  for  $1 
For  this  Policy  multiply  by  /..(?..... 

OOO  Insurance 

LOAN  OR  CASH 
SURRENDER  VALUES 

END  OF  EXTENSION 

ON  SURRENDER 

3d 

//)  Years  ^^Days 

$ 

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y  ? 

Should  any  indebtedness  exist  it  shall  be  deducted  from  the  Cash  Value  of  the  Policy, 
and  the  other  values  shall  be  diminished  proportionately 


LIFE   INSURANCE  415 

WRITTEN  EXERCISES 

1.  If  the  insured  in  the  foregoing  policy  should  die  just  be- 
fore the  twelfth  payment  was  due,  how  much  would  the  estate 
receive  above  his  total  payments  ? 

2.  Suppose  that  the  insured  in  the  foregoing  policy  survives 
the  endowment  period,  and  the  surplus  earnings  of  the  policy 
amounted  to  $ 3500.     What  would  be  the  difference  between  the 
amount  received  and  the  amount  paid,  not  reckoning  interest  ? 

3.  The  insured  in  the  foregoing  policy  took  out  a  110,000 
20-payment  life  policy  at  the  same  time  he  procured  his  endow- 
ment policy.     The  guaranteed  cash  value  on  the  former  was 
$ 2557.80  at  the  end  of  10  yr.,  and  the  dividends  for  this  term 
amounted  to  $83.22  per  thousand.     If  the  dividends  on  the 
endowment  policy  for  this  period  amounted  to  $  127.83  per  thou- 
sand, which  would  have  been  the  better  investment,  interest  not 
being  considered,  and  how  much  ? 

4.  Assuming  that  the  insured  in  the  foregoing  policy  survived 
the  endowment  period  and  that  the  dividends  which  amounted 
to  $350  per  thousand  were  used  to  add  to  the  value  of  the  pol- 
icy, how  much  less  would  he  receive  from  the  company  than  he 
would  from  investing  the  amount  of  the  premiums  in  a  savings- 
bank  annually  for  20  yr.  at  4  %  interest  ? 

5.  What  will  be  the  first  annual  premium  on  a  $15,000  ordi- 
nary life  policy  for  a  man  50  yr.  old  ? 

6.  On   his    25th  birthday  A  took  out  a   20-yr.  endowment 
policy    for   $5000  :    on    his    35th    birthday,    a    15-yr.  endow- 
ment policy  for  $6000;    on  his  40th  birthday,  a  20-payment 
life   policy  for  $10,000.     He  died  aged  43   yr.,  6  mo.     How 
much  more  did  his  heirs  receive  (dividends  excepted)  than  he 
had  paid  the  company  ? 

7.  B  at  the  age  of  25  yr.  took  out  a  20-payment  life  policy 
for  $5000.     He  died  just  before  his  twentieth  payment  became 
due.     The  company  allowed  $87.50  per  thousand  in  dividends 
during  this  period,  and  these  were  used  to  reduce  the  annual 
premium.     How  much  more  did  his  heirs  receive  than  was  paid 
in  premiums  ? 


PARTITIVE     PROPORTION,    PARTNERSHIP, 
AND     STORAGE 

CHAPTER   XXXV 

PARTITIVE  PROPORTION  AND   PARTNERSHIP 
PARTITIVE  PROPORTION 

ORAL   EXERCISE 

1.  A  fails  in  business  owing  D  $500,  E  $1500,  and  F  $2500. 
If  his  resources  are  $1800,  how  much  can  he  pay  each  of  his 
creditors  ? 

2.  Two  brothers,  A  and  B,  are  engravers.     A  can  earn  $10 
per  day  and  B  $5  per  day.     How  much  can  they  both  earn  in 
a  day  ?     What  part  of  this  amount  can  B  earn  ?     A  ? 

3.  They  formed  a  partnership  for  one  year  and  agreed  to 
divide  the  net  profits  in  proportion  to  the  earning  capacity  of 
each.     If  the  net  profits  for  the  year  were  $3600,  what  was  the 
share  of  each  ? 

4.  C  invests  $3000,  B  $6000,  arid  A  $9000  in  a  manufacturing 
plant.     The  net  profits  for  one  year  are  $3600,  and  this  sum  is 
shared  in  proportion  to  the  amount  of  capital  invested.     What 
amount  does  each  receive  as  his  share  of  the  net  profits  ? 

5.  A  certain  street  was  paved  at  a  cost  of  $3000.     The  prop- 
erty owners  on  the  street  were  A,  who  owned  200  ft.  frontage, 
B,  who  owned  400  ft.  frontage,  and  C,  who  owned  600  ft.  front- 
age.    If  the  cost  of  the  paving  was  assessed  on  the  property 
owners  in  proportion  to  the  frontage  owned,  how  much  did 
each  pay  ? 

493.    The  process  of  dividing  a  number  into  parts  propor- 
tional to  several  given  numbers  is  called  partitive  proportion. 

416 


PARTITIVE   PROPORTION   AND  PARTNERSHIP     417 
WRITTEN  EXERCISE 

1.  Divide  $42,770  among  G,  H,  and  I  in  proportion  to  ^,  £, 
and  -J,  respectively. 

SUGGESTION.     £,  |,  and  %  -  |,  j,  and  $,  respectively.     Therefore,  |,  $,  and 
|  stand  in  the  same  relation  to  each  other  as  f,  f,  and  £,  or  as  2,  4,  and  1. 

2.  Divide  the  simple  interest  on  f  72,000  for  1  yr.  7  mo.  at 
3J%  among  D,  E,  and  F  so  that  D's  part  will  be  twice  E's  part 
and  one  half  of  F's  part. 

3.  An  inheritance  of  $75,000  was  divided  among  3  sons  and 
4  daughters,  so  that  each  daughter  received  ^  more  than  each 
son.     How  much  did  each  son  receive  ?  each  daughter  ? 

4.  A,    B,   and    C   were   partners  in  a  business.     A   put  in. 
110,000,  B  16000,  and  C  $9000.     Their  net  gain  for  a  year  was 
$17,500,  shared  in  proportion  to  the  amount  of  capital  invested. 
What  was  each  partner's  share  of  the  net  gain  ? 

PARTNERSHIP 

ORAL  EXERCISE 

1.  I  invested  $  500  in  a  business  and  during  the  first  year 
gained   $1100.     No   withdrawals   or   subsequent   investments 
having  been  made,  what  was  my  present  worth  at  the  close  of 
the  year  ? 

2.  Jan.   1  M  invested  $  7500  in  a  factory.     July  1  he  found 
that   his  net  loss  was  $  1125.       What  was  his  present  worth 
July  1,  no  withdrawals  or  subsequent  investments  having  been 
made  ? 

3.  Answer  problem  1  assuming  that  there  was  a  withdrawal 
of  $  800  made  during  the  year ;  problem  2  assuming  that  there 
was  a  subsequent  investment  of  $  1200  made  on  Mar.  1. 

4.  Apr.  1  B  commenced  business  with  a  cash  investment  of 
$  1500  ;  Jan.  1  of  the  next  year  his  present  worth  was  $  1875. 
What  was  his  net  gain  or  loss,  no  withdrawals  or  subsequent 
investments  having  been  made  ? 


418  PRACTICAL   BUSINESS   ARITHMETIC 

5.  July  1  D  began  business  investing  125,000;  Jan.  1  of 
the  next  year  his  net  capital  was  $  23,150.     If  no  withdrawals 
or  subsequent  investments  were  made,  did  he  gain  or  lose,  and 
how  much  ? 

6.  Answer  problem  4  assuming  that  there  were  withdrawals 
amounting   to  $  1000  ;   problem  5  assuming  that  there  was  a 
subsequent  investment  of  $5000. 

7.  June    1    F    began  business   with   a    capital    of   $ 1750. 
During  the   6  mo.    following  he  lost  $  2750.     What  was  the 
condition  of  his  business  Dec.  1  ? 

8.  Z  began  business  on  July  1  with  a  capital  of   $  2500. 
6  mo.  later  his  net  insolvency  was  found  to  be  $  1250.     What 
was  his  net  gain  or  loss  ? 

9.  A's    business  was   insolvent   $  1250  on   Jan.  1.     From 
Jan.  1  to  July  1  he  gained  $  1750.     What  was  the  condition 
of  his  business  July  1  ? 

10.  G  gained  $  3750  during  a  certain  year.     He  then  found 
that  his  net  capital  was  $1250.     What  was  the  condition  of 
his  business  at  the  beginning  of  the  year  ? 

11.  June  30,  1906,  C's  resources  were  I  7500  and  his  liabili- 
ties $  5000.     June  30,  1907,  his  resources  were  $  5000  and  his 
liabilities  $  7500.     What  was  his  net  gain  or  loss  during  this 
period  ? 

12.  Were  the  conditions  in  problem  11  reversed  for  the  year 
stated,  what  would  be  the  net  gain  or  loss  ? 

13.  What  is  meant  by  resources?   liabilities?  gain?   loss? 

14.  What  is  meant  by  net  gain?    net  loss?  present  worth? 
net  capital?   net  insolvency? 

15.  Read  aloud  the  following,  supplying  the  missing  words: 
The  condition  of  the  business  at  the  beginning  -f  the 

or  —  the  =  the  condition  of   the  business   at  the 

close  ;    and    conversely,  the  condition   of   the  business  at  the 

close  H-  the or  —  the =  the  condition  of 

the  business  at  the  beginning. 


PARTITIVE   PROPORTION   AND   PARTNERSHIP     419 

494.  A  partnership  is  an  association  of  two  or  more  persons 
who  have  agreed  to  combine  their  labor,  property,  and  skill, 
or  some  of  them,   for  the  purpose  of    carrying  on  a  common 
business  and  sharing  its  gains  and  losses. 

Partnerships  may  be  formed  by  either  an  oral  or  a  written  agreement,  and 
in  some  cases  by  implication  ;  but  all  important  partnerships  should  be 
entered  upon  by  an  agreement  in  writing  which  definitely  states  all  of  the 
conditions  relating  to  the  business. 

495.  The  members  of  a  partnership  are  called  partners. 

Partners  may  be  divided  into  four  classes:  (1)  Real,  or  ostensible,  those 
who  are  known  to  the  world  as  partners  and  who  in  reality  are  such; 
(2)  nominal,  those  who  are  known  to  the  world  as  partners  but  who  have 
no  investment  and  receive  no  share  of  the  gain  ;  (3)  dormant,  or  silent, 
those  who  are  not  known  to  the  world  but  who  nevertheless  partake  of  the 
benefits  of  the  business  and  thereby  become  partners ;  (4)  limited,  or 
special,  those  whose  liability  is  limited. 

Nominal  partners,  like  real,  or  ostensible,  partners,  are  liable  to  third 
parties  for  the  debts  of  a  business.  Dormant  partners  are  liable  for  the 
debts  of  the  business  as  soon  as  their  partnership  connections  become  known 
to  the  world. 

Ordinarily  each  partner  is  liable  for  all  of  the  debts  of  the  firm,  but  a 
special  partner's  liability  is  limited  usually  to  the  amount  which  he  con- 
tributes to  the  firm's  capital. 

The  method  of  forming  a  limited  partnership  is  prescribed  by  statute. 
This  differs  somewhat  in  the  different  states.  Such  a  partnership  must 
usually  have  at  least  one  member  whose  liability  is  not  limited  and  who  is 
the  manager  of  the  business. 

496.  The  capital  of  a  partnership  constitutes  all  the  moneys 
and  other  properties  contributed  by  the  different  partners  to 
carry  on  the  business. 

GAINS  AND  LOSSES  DIVIDED  EQUALLY 

497.  The  gains  and  losses  of  a  business  are  divided  among 
the  partners  in  accordance  with  the  agreement  or  contract  en- 
tered into  when  the  partnership  was  formed.     If  the  partners 
invest  equal  sums  and  contribute  equally  in  work,  the  gains  are 
usually  divided  equally. 


420 


PRACTICAL    BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 

l.    Copy  and  complete  the  following  ledger  page : 


30 


Jo 


,7cf? 


!&4 


t^Z^Si^^^^^i^ 


^W-**-d<^^-7-2-£'*Z^ 


J~006 


ff 


In  solving  problems  2-4  use  ledger  paper  as  above. 

If  the  student  is  not  familiar  with  simple  accounts,  pages  41-47  should 
be  reviewed. 

2.  Jan.  1,  1907,  C.  B.  Johnson  and  B.  H.  Briggs  engaged  in 
a  partnership  business,  each  investing  $3750.  July  1,  1907, 
each  partner  withdrew  $  250.  Jan.  1,  1908,  their  losses  and 
gains  were  as  follows  : 

LOSSES  GAINS 

Expense  $104.75  Merchandise  $628.45 

Merchandise  Discounts  24.20  Interest  and  Discount  133.50 

Real  Estate  250.60  Stocks  and  Bonds  190.50 


What  was  the  present  worth  of  each  partner  Jan.  1,  1908  ? 


PARTITIVE   PROPORTION   AND   PARTNERSHIP     421 

3.  A,  B,  and  C  were  partners  for  a  year.     Each  invested 
$9500  and  during  the  continuance  of  the  partnership  each  with- 
drew $1000.    The  losses  and  gains  at  closing  were  as  follows  : 

LOSSES  GAINS 

Merchandise  Discounts  $18.90      Merchandise  $4375.80 

Expense  650.00      Interest  and  Discount  90.14 

What  was  the  net  capital  of  each  at  closing? 

4.  O,  P,  and  Q  are  partners  sharing  the  gains  and  losses  in 
equal  proportions.     O  invested  18500,  P  18200,  and  Q  18450. 
During  their  first  year  the  gains  were  as  follows :  merchandise, 
16457.10  ;  real  estate,  1680.50  ;   interest  and  discount,  $29.90. 
If  the  cost  of  conducting  the  business  was  $1920.50,  what  was 
the  present  worth  of  each  partner  at  the  end  of  the  year  ? 

GAINS  AND  LOSSES  IRREGULARLY  DIVIDED 

498.  Sometimes  the  gains  are  divided  according  to  certain 
arbitrary  fractions  which  are  riot  in  proportion  to  the  amount 
invested.  In  such  cases  the  skill  of  a  partner  is  frequently 
considered  as  being  equal  to  a  certain  amount  of  capital.  In 
some  cases  a  certain  amount  is  paid  the  heavier  investor 
before  other  division  of  the  gains  or  losses  is  made.  In  still 
other  cases,  a  stated  salary  is  paid  to  each  partner  before  the 
gains  or  losses  of  the  business  are  divided.  This  salary  varies 
according  to  the  ability  of  the  several  partners  or  according  to 
the  time  each  devotes  to  the  business. 

WRITTEN  EXERCISE 

l.  A  and  B  entered  into  partnership,  each  investing  $7500. 
Because  of  the  greater  experience  of  A  he  was  to  be  credited 
with  $1200  before  any  other  division  of  the  gains  or  losses. 
The  gains  or  losses  were  then  to  be  divided  equally.  During 
the  first  year  the  gains  were  as  follows  :  merchandise,  $4111.10  ; 
real  estate,  $510.  If  the  losses  were  $622.80,  what  was  the 
present  worth  of  each  at  the  end  of  the  year? 


422  PRACTICAL   BUSINESS   ARITHMETIC 

2.  A  and  B  entered  into  partnership,  A  investing  $  8000  and 
B  '$10,000.     B  doing  no  work,  it  was  agreed  that  A  should  take 
$  2000  from  the  gains  before  dividing,  and  that  the  net  gain  or 
loss  should  then  be  shared  equally.     The  gains  last  year  were 
18900  and  the  losses  11400.     What  was  the  net  gain  of  each? 

3.  C,  D,  and  E  entered  into  partnership  Jan.   1,   each  in- 
vesting $8500.     The  articles  of  agreement  provided  (1)  that 
C  should  devote  all  his  time  to  the  business  and  D  and  E  only 
a  portion  of  their  time  ;   (2)  that  if  losses  occurred,  they  should 
be  borne  equally  ;   (3)  that  if  gains  were   realized,  C   should 
receive  \  and  D  and  E  each  ^.      During  the  year  the  gains 
were  as  follows:  Merchandise,   $8217.10;  Stocks  and  Bonds, 
$612.50;   Interest,  $492.92.     If  the  expenses  were  $2217.80, 
what  was  the  present  worth  of  each  partner  at  the  close  of  the 
year  ? 

4.  F  and  G  entered  into  partnership,  F  investing  $5000  and 
G  $7500.     Because  of  the  greater  skill  of  F  it  was  agreed  that 
he  should  be  credited  with  $  1500  a  year  before  other  division  of 
the  gains  or  losses.    Then  if  losses  occurred,  F  was  to  bear  |  of 
them   and  G  ^  ;  but  if  gains  were  realized,  they  were  to  be 
divided  equally.     During  the  first  year  the  gains  of  the  firm 
were  as  follows  :  Merchandise,  $3129.50  ;   Real  Estate,  $250  ; 
Stocks  and  Bonds,  $575;    Interest,  $130.50.     If  the  cost  of 
conducting  the  business  was  $938.48  (exclusive  of  F's  salary), 
what  was  each  partner's  net  capital  at  the  close  of  the  year  ? 

5.  J,    K,    and    L    entered    into     partnership,    J    investing 
$20,000,  K  $10,000,  and  L  nothing.     The  articles  of  agreement 
provided    (1)    that   the  gains   or  losses    should   be  shared  as 
follows  :   J,  f,  K,  ^,  L,  23o  5   (2)  that  the  capital  should  be  kept 
intact  ;    (3)  that  before  any  division  of  the  profits  was  made,  J 
should  be  credited  with  an  annual  salary  of  $1500.     At  the 
end  of  a  year  the  resources  were  found  to  be  $65,250  and  the 
liabilities  (not  including  J's  salary),  $16,750.     What  was  each 
partner's    share    of   the   net   gain  ?     After   the  net   gain  was 
credited,  what  was  the  net  capital  of  each  partner  ? 


PARTITIVE   PROPORTION    AND   PARTNERSHIP     423 

GAINS  AND  LOSSES  DIVIDED    ACCORDING   TO   INVESTMENT 

499.  Sometimes  the  gains  and  losses  are  divided  in  propor- 
tion to  the  amount  invested  ;  that  is,  according  to  the  princi- 
ples of  partitive  proportion. 

500.  Example.    A  and  B  engaged  in  business,  agreeing  to 
share  the  gains  or  bear  the  losses  in  proportion  to  the  amount 
of  capital  invested.     A  invested  12500  and  B  13500.     They 
gained  $1800.     What  was  the  share  of  each? 

SOLUTION.  $2500  +  $  3500  =  $  6000,  the  total  capital.  Since  the  total  capital 
is  $6000  and  A  put  in  $2500,  A's  share  is  $$#,  or  T\,  and  B's  share  is  ff{$,  or 
r7z.  Therefore,  A  should  receive  T\  of  $  1800,  or  $750,  and  B  should  receive 
&  of  $  1800,  or  $  1050. 

ORAL   EXERCISE 

Find  each  mans  gain  or  loss  in  each  of  the  following  problems : 
INVESTMENT  GAIN  INVESTMENT  Loss 

1.  A,  $ 3000;   B,  12000     $500  6.  K,$2000;   L,$4000  $120 

2.  C,  11000;  D,  12000     $150  7.  M,$1500;  N,  $2000  $700 

3.  E,  $1200;  F,  $4800   $1200  8.  O,$1000;  P,$5000  $600 

4.  G,$1500;  H,  $4500  $1800  9.  Q,$1500;  R,$6000  $750 

5.  I,  $1500;  J,  $7500  $1500  10.  S,  $1750;  T,$3500  $600 

WRITTEN   EXERCISE 

1.  A,  B,  and  C  invested  $2000,  $3000,  and  $5000,  respec- 
tively, in  a  wholesale  dry  goods  business.     During  the  first  year 
the  net  profits  were  $4155.80.     What  was  the  share  of  each  ? 

2.  D,  E,  and  F  invested  $2500,  $3250,  and  $3500,  respec- 
tively, in  a  manufacturing  business.     At  the  close  of  the  first 
year  their  profits  were  found  to  be  $3774.37.     What  was  the 
share  of  each  ? 

3.  G,  H,  and  I  formed  a  copartnership,  G  investing  $3000, 
H,  $2000,  and  I,  $1500.     During  the  first  six  months  their  net 
gain  was  $1829.10.     How  much  was  each  man  worth  after  his 
share  of  the  net  gain  had  been  carried  to  his  account  ? 


424  PRACTICAL   BUSINESS   ARITHMETIC 

4.    Copy  and  complete  the  following  statement : 


PARTITIVE   PROPORTION   AND   PARTNERSHIP     425 


INTEREST  ALLOWED  AND  CHARGED 

501.  The  inequalities  in  investments  and   withdrawals  are 
frequently  adjusted   by  allowing  and  charging   interest  upon 
same.     When  interest  is  allowed  and  charged  on  investments 
and    withdrawals,   the    gains    and   losses    are    usually    divided 
equally. 

502.  Example.    June  1,  1907,  C.  H.  Dean  and  E.  D.   Snow 
formed  a  partnership,  C.  H.  Dean  investing  $5000  and  E.  D. 
Snow  $  4000.     They  agreed  that  the  gains  and  losses  should  be 
divided  equally,  but  that,  owing  to  the  unequal  investments, 
each  partner  should  be  allowed  interest   at  6  %   on  all  sums 
invested  and  charged  interest   at  the   same  rate   on   all  sums 
withdrawn,  said  interest  to  be  adjusted  at  the  time  of  closing 
the  books.     The  profits  for  the  first  six  months   were  $  1050. 
What  was  the  net  capital  of  each  partner  after  the  interest  was 
adjusted  and  the  net  gain  carried  to  his  account  ? 

C.  H.  DEAN 


1906 
Dec. 

1 

Net  Capital 

5540 

00 

1906 

June 
Dec. 

1 
1 
1 

Investment 
Interest 
\  Net  Gain 

Net  Capital 

5000 
15 
525 

00 
00 
00 

5540 

00 

5540 

00 

Dec. 

1 

5540 

00 

E.    D.    SNOW 


1SI07 

I 

1907 

Dec. 

1 

Interest 

15 

00 

June 

1 

Investment 

4000 

00 

1 

Net  Capital 

4510 

00 

1 

i  Net  Gain 

525 

00 

4525 

00 

4525 

00 

~l 

Dec. 

1 

Net  Capital 

4510 

00 

SOLUTION.     $  5000  in  6  mo.  will  earn  $  150  interest.     $  4000  in  6  mo.  will  earn 


$120  interest.  S 150  +  $  120  -H  2  =  $135,  the  average  interest  earned. 
$  150  -  $  135  =  $  15  ;  that  is,  C.  H.  Dean's  interest  is  $  15  above  the  average. 
$  135  —  $ 120  =  $  15  ;  that  is,  E.  D.  Snow's  interest  is  $15  below  the  average. 
Therefore  to  adjust  the  interest  on  the  investments,  credit  C.  H.  Dean's  ac- 
count $  15  and  charge  E.  D.  Snow's  account  $  15.  ^  of  $  1050  =  $  525,  the  net 
gain  of  each.  Credit  each  account  with  the  net  gain  ;  then  C.  II.  Dean's  net 
capital  is  $5540  and  E.  D.  Snow's  net  capital  $4510. 


426  PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 


1.    Copy  and  complete  the  following  statement  of  conditions 

QZ^zfys^^ 


it  „ 


43  &S 


2-0  &c*J 


2-2.  e>y 


?  2.  Of 


fo 


PARTITIVE   PROPORTION   AND   PARTNERSHIP     427 

2.  W.  H.  Burgess  and  Otis  Clapp  began  business  July  1, 
1906,   the  former  investing  112,000  and  the  latter  110,000. 
They  agreed  that  the  gains  and  losses  should  be  divided  equally, 
but  that,  because  of  the  inequality  in  the  investments,  interest 
at  6  %  should  be  allowed  on  investments  and  charged  on  with- 
drawals.    July    1,    1907,    the    firm's   resources   and    liabilities 
(partners'  accounts  excluded)  were  as  follows  : 

RESOURCES  LIABILITIES 

Cash  $4150.00      Accounts  Pay.                            $7500. 

Accounts  Rec.  8150.60      Notes  Pay.                                     4900. 

Mdse.  18210.50 

Notes  Rec.,  on  hand  4250.00 

Street  Railway  Stock  3000.00 

Store  and  Lot  5200.00 

Office  Fixtures  500.00 

Make  a  statement,  as  in  problem  1,  showing  the  present  con- 
dition of  the  business. 

3.  Aug.  1,  1906,  F.  E.  Greene  and  W.  B.  Linden  formed  a 
partnership  for  the  purpose  of   carrying  on  a  manufacturing 
business.     F.  E.  Greene  invested   $8500    and  W.   B.  Linden, 
$10,750.     It  was  agreed  that  interest  at  6%  should  be  allowed 
and  charged  on  investments  and  withdrawals  and  that  the  gains 
and  losses  should  be  divided  equally.     At  the  close  of  the  first 
year  the  resources  and  liabilities  (partners'  accounts  excluded) 
were  as  follows : 

RESOURCES  LIABILITIES 

Cash  12355.20      Notes  Pay.  $1158.25 

Mdse.  5284.85      Accounts  owed  by  the  busi- 

Notes  Rec.  2840.00          ness  2100.00 

Accounts  owing  the  business  4170.50 
Office  Fixtures  450.00 

Feb.  1,  1907,  F.  E.  Greene  withdrew  $750  and  W.  B.  Linden 
$600.  Make  a  statement  showing  the  condition  of  the  business 
at  the  close  of  the  year. 

4.  James  B.  Westfall  and  John  L.  Manning  began  a  common 
business  on  Sept.   1,  1906,  the  former  investing  $14,500  and 
the  latter  $13,935.     They  agreed  that  interest  at  6/0  should  be 


428  PRACTICAL   BUSINESS   ARITHMETIC 

allowed  and  charged  on  investments  and  withdrawals,  respec- 
tively, and  that  the  gains  and  losses  should  be  divided  equally. 
Sept.  1,  1907,  a  trial  balance  of  their  general  ledger  was  as 

follows  : 

DEBITS  CREDITS 

James  B.  Westfall  $14500.00 

John  L.  Manning  13935.00 

Cash  $13368.64 

Merchandise  31664.00                 20000.00 

Office  fixtures  510.50 

Horse  and  wagon  405.00 

Real  estate  7000.00 

Expense  445.80 

Collection  and  exchange  12.20 

Mdse.  discounts  58.50 

Accounts  receivable  6852.84 

Accounts  payable  8864.75 

Bills  payable  3000.00 

Interest  and  discount  17.73 

$60317.48  $60317;48 

The  merchandise  unsold  was  found  to  be  worth  113,827.35  ; 
the  real  estate,  $7500  ;  the  office  fixtures,  1500  ;  the  horses  and 
wagons,  $ 400;  and  the  expense  items  on  hand,  §102.50.  There 
was  due  on  the  merchandise  account  for  freight,  $138.50,  and 
on  the  expense  account  for  telephone  service,  $25.  Make  a 
statement  showing  the  condition  of  the  business  Sept.  1,  1907. 
(See  model,  page  431.) 

GAINS  AND  LOSSES  DIVIDED  ACCORDING  TO  THE  AVERAGE 

INVESTMENT 

503.  That  sum    which,    invested    for    a    certain    period,    is 
equivalent  to  two  or  more  sums  invested  for  different  periods, 
is  called  an  average   investment.     The  gains  and  losses  of  a 
business  are  sometimes  divided  in  proportion  to  the  average 
investment. 

504.  Example.    April  1,   1906,  A  and   B  formed  a  partner- 
ship and  agreed  to  share  the  gains  or  losses  according  to  aver- 
age net  investment.     A  furnished  $10,000  of  the  capital  and 


PARTITIVE   PROPORTION  AND   PARTNERSHIP     429 

B  17500.  July  1  A  withdrew  11500  and  B  $500.  Apr.  1, 
1907,  their  net  gain  was  found  to  be  112,800.  What  was 
the  net  gain  of  each  partner? 

SOLUTION 

A  had  in  $10,000  for  3  mo.,  when  he  withdrew  $1500,  leaving  $8500  for  the 
remaining  9  mo. 

B  had  in  87500  for  3  mo.,  when  he  withdrew  $500,  leaving  $7000  for  the 
remaining  9  mo. 

A's  $10000  for  3  mo.  =  $30000  for  1  mo. 

A's  $8500  for  9  mo.  =  $76500  for  1  mo. 

A's  average  net  investment  =  $  106500  for  1  mo. 

B's  $7500  for  3  mo.  =  $22500  for  1  mo. 

B's  $  7000-  for  9  mo.  =  $63000  for  1  mo. 

B's  average  net  investment     =  $85500  for  1  mo. 
$  106500  +  $85500  =  $192000,  the  firm's  average  net  investment  for  1  mo. 

A's  share  is  i|f^,  or  ^V 

B's  share  is  TW<&V  or  r52V 

Therefore,  A  should  receive  Ty*  of  $12800,  or  $7100. 

And  B  should  receive  ^  of  $12800,  or  $5700. 

WRITTEN  EXERCISE 

1.  Apr.    1    R   and   C    formed   a  partnership  for  1  yr.,  the 
former  investing  $4500  and  the  latter  16000.     They  agreed 
to  share  the  gains  and  losses  in  proportion  to  the  average  net 
investment.    Aug.  1  R  invested  $1500,  and  C  withdrew  $1000. 
On  closing  the  books  at  the  end  of  the  year  the  net  loss  was 
found  to  be  $1290.      What  was  each  partner's  present  worth 
after  his  account  was  charged  with  his  share  of  the  net  loss  ? 

2.  June  1,  1906,   E  and  F  formed  a  copartnership  for  the 
purpose  of  carrying    on   a  real  estate   business.     E   invested 
$25,000  and  F  $15,000.     They  agreed  to  share  the  gains  and 
losses  in  proportion  to  the  average  net  investment.     Sept.  1, 

1906,  E  withdrew  $1000    and  F  $500.     Dec.    1,  1906,  each 
withdrew  $1000.     Mar.  1,  1907,  F  invested  $5000.     June  1, 

1907,  the  partnership  was  dissolved.     After  all  resources  were 
converted  into  cash  and  all  liabilities  to  outside  parties  paid, 
the  amount  of  cash  in  bank  was  $  50,890.     What  amount  was 
due  each  partner? 


430  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN  REVIEW   EXERCISE 

1.  Apr.  1,  1907,  W.  L.  Cutter  and  O.  M.  Woodward  formed 
a  copartnership  for  the  purpose  of  carrying   on  a  dry  goods 
business.     W.  L.  Cutter  invested  820,500  and  O.  M.  Wood- 
ward  $18,500.       They   agreed   to   allow   interest   at   6%    on 
investments,  charge  interest  at  the  same  rate  on  withdrawals, 
and  divide  the  gains  and  losses  equally.     July  1,  1907,  W.  L. 
Cutter  withdrew  1 500.     Oct.  1  O.  M.  Woodward  withdrew 
$1000  and  W.  L.  Cutter  $750.     At  the  close  of  the  year  the 
resources  and  liabilities,  exclusive  of  partners'  accounts,  were 
as  follows  : 

RESOURCES  LIABILITIES 
Cash  in  bank  $2130.60      Accounts  owed  by  the  busi- 
Stocks  and  bonds  on  hand  6450.00          ness                                      $7260.00 
Goods  in  stock  16095.00      Notes  payable  unredeemed     1200.00 
Notes  receivable  on  hand  6150.00 
Office  fixtures  on  hand  500.00 
Accounts  owing  the  busi- 
ness 12260.52 

Make  a  statement  showing  the   condition  of   the  business 
Apr.  1.  1908. 

2.  July  1,  1906,  A.  B.  Curtis  and  B.   H.   Barton  formed  a 
partnership  and  invested  $  7500,  of  which  A.   B.   Curtis  fur- 
nished |  and  B.  H.  Barton,  -|.     Jan.  30,  1907,  their  resources 
were   as  follows:    merchandise,    unsold,    $2172.70;     cash   on 
hand,  $2823.96;  real  estate  on  hand,  $3100;  account  against 
James  Noble,   $840.10;  account  against  A.   H.   Cook   &   Co., 
$  1156.84.     On  the  same  date  their  liabilities  were  as  follows  : 
account   in  favor  of  D.   M.   Frost  &   Co.,  $218.60;    account 
in   favor   of  J.   B.  Neal  &  Co.,  $385.     During  the  year  the 
merchandise  bought  cost  $6807.50  and   the  sales  aggregated 
$7154.90.     The  cost  of  carrying  on  the  business  was  $530.10. 
Make  a  statement  (see  page  424)  showing  the  present  condi- 
tion of  the  business.     Divide  the  net  gain  in  proportion  to  the 
investments. 


PARTITIVE   PROPORTION   AND   PARTNERSHIP     431 
3.    Copy  and  complete  the  following  statement  of  conditions: 


432  PRACTICAL   BUSINESS   ARITHMETIC 

4.  Jan.  1,  1906,  C.  H.  Smith  and  W.  W.  Osgoodby  formed 
a  copartnership  for  the  purpose  of  carrying  on   a  real  estate 
business.     C.  H.  Smith  invested  115,000  and  VV.  W.  Osgoodby 
%  10, 000.     They  agreed  to  share  the  gains  and  losses  in  pro- 
portion  to  the   average  net  investment.     July  1,  1906,  C.    H. 
Smith  withdrew  $1000  and  W.  W.  Osgoodby  $750.     On  clos- 
ing the  books  at  the  end  of  the  year  the  net  gain  was  found  to 
be  $8685.      What  was  each  partner's  present  worth  after  his 
account  was  credited  with  his  share  of  the  net  gain? 

5.  Frank  M.  Congdon,  E.  H.  Robinson,  and  O.  B.  Moulton 
are   partners   in    a   dry  goods  house  under   the  firm    name  of 
E.  H.  Robinson  &  Co.     On  commencing  business  Aug.  1,  1901, 
Frank  M.  Congdon  invested  $17,500,  E.  H.  Robinson  $20,000, 
and  O.   B.   Moulton  $12,000.     The  articles  of  agreement  pro- 
vided :   (1)  that  each  partner  should  be  allowed  interest  at  6% 
on  investments  and  charged  interest  at  the  same  rate  on  with- 
drawals ;     (2)    that    because    of   special    skill    and    experience 
Frank  M.  Congdon  should  be  credited  $1500  before  any  other 
division  of  the  gains  and  losses ;    (3)  that  then  the  gains  should 
be  divided  equally.     Aug.   1,  1908,  the  results  of  the  year's 
business    were    as    follows  :     cost    of   merchandise    purchased, 
$81,240;   value  of  merchandise  on  hand,  $14,280.95;  sales  of 
merchandise,   $78,756;    cost  of  real   estate,   $18,000;    cost  of 
permanent  improvements  on  real  estate,  $1200;   present  esti- 
mated value  of  real  estate,  $25,000;  notes  in  favor  of  the  firm, 
$11,500;  interest  accrued  on  these  notes,  $112;  cost  and  pres- 
ent value  of  horses  and  wagons,  $  1250 ;   general  expenses  for 
the  year  (exclusive  of  the  amount  due  Congdon),  $1800  ;  trav- 
eling expenses  for  the  year,  $1200;   accounts  owing  the  firm, 
$20,160.90;   cash  on  hand,  $19,033.10;   mortgage  on  the  firm's 
real  estate,  $12,000;  interest  accrued  on  the  mortgage,  $480; 
notes  outstanding,  $3500;   accounts  owed  by  the  firm,  $11,260. 
Show    in    proper    statements    the    financial    condition    of   the 
partners. 


CHAPTER   XXXVI 

STORAGE 
SIMPLE   STORAGE 

ORAL  EXERCISE 

1.  I  stored  my  piano  in  a  warehouse  from  June  16  to  Octo- 
ber 1  at  $1  per  month  or  fraction  thereof.     What  sum  must  I 
pay  in  settlement  ? 

2.  I  rented  a  room  in  a  storage  warehouse  from  Sept.  1  to 
Dec.  18  at  §6.50  per  month  or  fraction  thereof.     What  amount 
did  I  have  to  pay  ? 

3.  What  must  I  pay  for  the  storage  of  5000  bu.  of  wheat 
stored  from  Dec.  3  to  Apr.  15  at  4^  per  bushel  per  month  or 
fraction  thereof  ?    for  the  storage  of  10,000  bu.  of  corn  stored 
from  Dec.  1  to  Mar.  1  at  3^  per  bushel  per  month  ? 

505.  Storage  is  a  charge  made  for  storing  goods  in  a  ware- 
house. 

506.  The  term  of  storage  is  the  period  of  time  for  which  a 
certain  rate  is  charged. 

The  term  of  storage  is  usually,  though  not  invariably,  30  da. ;  and  in 
estimating  charges,  a  part  of  a  term  is  counted  the  same  as  a  full  term. 

507.  The  rates  of  storage  are  sometimes  fixed  by  an  agree- 
ment between  the  contracting  parties,  sometimes  by  boards  of 
trade,  chambers  of  commerce,  or  associations  of  warehousemen, 
and  sometimes  by  legislative  enactment. 

508.  Simple  storage  is  storage  estimated  at  the  time  of  the 
withdrawal  of  the  goods  from  the  warehouse. 

433 


434 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

1.    Verify  the  following  storage  bill: 


To  Quincy  Market  Cold  Storage  and  Warehouse  Co.,  Dr 

Main  Office,  133  Commercial  Street 


FOR   STORAGE 


DATE 
RECEIVED 

QUANTITY 

MERCHANDISE 

STORAGE 
LOT  NO. 

DATE 
DELIVERED 

QUANTITY 

MO. 

RATE 

AMOUNT 

$a&. 

/-^ 

£22 

-r^t. 

£tZ^f 

z^T4^T 

-^y^ 

^ 

/^/7 

^^ 

_^£ 

^ 

c£2 



' 

'ti'W 

?(, 

2^2 

/*V7 

„ 

(Lm 

J 

££2 

<P^( 

/?-# 

_ 

,?/£ 

_ 

V 

^ 

2.  When  were  the  eggs  received  for  storage  ?     If  there  are 
30  doz.  in  a  case,  how  many  dozen  were  received '? 

3.  Suppose  the  rate  in  the  bill  were  10^  per  case  per  month 
or   fraction  thereof  for   the   first  3  mo.,  and  5^  per  case  per 
month  after  the  first  3  mo.     What  would  this  rate  be  for  4  mo.  ? 
for  1  mo.  ?    for  9  mo.  ?    for  10  mo.  t    for  11  mo.  ? 

4.  Using  the  rate  in  the  bill,  find  the  storage  on  150  cs.  eggs 
stored  from  July  1  to  Jan.   14  ;  on  500  cs.  eggs  stored  from 
July  3  to  June  14 ;  on  350  cs.  eggs  stored  from  June  14  to 
Mar.  4  ;  on  12,000  doz.  eggs  stored  from  June  14  to  Nov.  18. 

5.  The  storage  rate  on  poultry  is  ^  ^  per  pound  per  month. 
Find  the  storage  on  1000  lb.  from  Jan.  10  to  Feb.  6  ;  on  800 
Ib.  from  Jan.  10  to  Feb.  18  ;  on  1200  lb.  from  Jan.  10  to  May 
27  ;  011 1600  lb.  from  Jan.  10  to  July  3. 

6.  In  a  certain  warehouse  the  rate  of  storage  on  cheese  is  8  ^ 
per  100  lb.,  for  each  month  or  fraction  thereof.     At  that  rate 
find  the  storage  on  1000  lb.  cheese  from  May  3  to  July  15  ;  on 
20,000  lb.  from  May  3  to  Aug.  26  ;  on  7500  lb.  from  May  3  to 
Sept.  12 ;  on  10,000  lb.  from  May  3  to  Oct.  6  ;  on  5  T.  from 
June  15  to  Oct.  28 ;  on  10  T.  from  June  15  to  Nov.  17. 


STORAGE 


435 


509.  Example.  The  following  memorandum  of  flour  stored 
for  you  by  the  Central  Storage  Co.  :  received  Nov.  1,  2000  bbl., 
and  Nov.  16,  3000  bbl.  ;  delivered  Nov.  8, 1000  bbl.,  and  Dec.  5, 
4000  bbl.  If  the  rate  of  storage  was  5^  per  barrel  per  month 
or  fraction  thereof,  what  was  the  bill  to  render? 


SOLUTION 

RECEIPTS  AND  DELIVERIES 
Nov.    1,  received  2000  bbl. 
Nov.    8,  delivered  1000  bbl.,  which  were  in  storage 

1000  bbl.,  balance  in  storage 
Nov.  16,  received   3000  bbl. 

4000  bbl.,  balance  in  storage 

Dec.  5,  delivered  4000  bbl.,  1000  of  which  were  in  storage  34  da.   10  t 
3000  of  which  were  in  storage  19  da.     5  ^ 
Total  storage, 


TERM  RATE  STORAGE 


7  da.     5  f      $50 


100 

150 

$  300 


WRITTEN  EXERCISE 

1.  In  a  certain  warehouse  the  storage  charges  on  flour  are  3  ^ 
per  barrel  per  month  or  fraction  thereof.      Nov.  1,  I  stored  500 
bbl.  ;   Dec.  1,  I  withdrew  100  bbl.  ;  Jan.  1,  I  stored  600  bbl.  ; 
Mar.  1,  I  withdrew  1000  bbl.     What  was  the  storage  on  the  first 
withdrawal  ?    400  bbl.  of  the  second  withdrawal  was  in  storage 
for  how  many  months  ?     What  was  the  total  storage  due  Mar.  1  ? 

2.  How  much  is  due  on  the  following  account? 


ton,  Mass.,, 


Received  from   (/?. 


.19. 


DELIVERIES  AND  CHARGES 

CREOITS 

DATE 

QUANTITY 

MONTHS 

RATE 

AMOUNT 

AMOUNT 

DATE 

REMARKS 

•^ 

3 

J= 

^^ 

MM* 

/ 

^^ 

^ 

?    7 

//. 

r^ 

-&/- 

^ 

^^ 

(2 

/?**# 

2- 

^^ 

? 

/s2>it?^?j 

/?     /? 

(^fsL^sif 

£ 

'tori 

^    / 

?    7 

,, 

7" 

M™# 

? 

^     ^ 

, 

~ 

' 

436 


PRACTICAL   BUSINESS   ARITHMETIC 


3.  The  following  is  a  memorandum  of  apples  stored  by  you 
for  T.  B.  Welch  &  Co.  :  received  Nov.  28,  5000  bbl.,  Dec.  15, 
1000  bbl.,  and  Dec.  18,  3000  bbl.;  delivered  Dec.  28,2000  bbl., 
Feb.  1,  1000  bbl.,  and  Feb.  10,  6000  bbl.     Render  a  bill  for 
the  storage,  charges  being  5^  per  barrel  per  month  or  fraction 
thereof. 

4.  Copy  and  complete  the  following  bill : 


To  EASTERN  COLD  STORAGE  CO.,  Dr. 

28  to  44  North  Street 

FOR  STORAGE 


LOT 

DATE 

NO. 
MONTH 

ARTICLE 

WEIGHT 

RATE  PER 

100  LB. 

EXTEN- 
SION 

AMOUNT 

IN 

OUT 

•7J&2 

&PT. 

'fl 

-£* 

A. 

4- 
q. 

,? 

/ 

2^?^^;£2^Z2^ 

/aaa/yj 

/^/ 

tffa. 

,   •? 

/f7  /?     f,                      f. 

<J~0aa$ 

JVt 

??7^ 

,4- 

3J7>    r 

'7.4730-6 

<?0  <£ 

ytssujL 

jjT 

A-T/9     ff             ,. 

yj-004 

tfrtfi 

— 

\ 

AVERAGE   STORAGE 

510.  When   there  are  frequent  receipts   and   deliveries  of 
goods,  it  is  customary  for  some  warehouses  to  average  the  time 
and  charge  a  certain  rate  per   month   of   thirty   days.     The 
process  is  called  average  storage. 

511.  Example.    The  following  is  a  memorandum  of  the  re- 
ceipts and  deliveries  of  flour  stored  by  the  Eastern  Storage  Co. 
for  A.  M.  Briggs  &  Co. :  received  Apr.  10,  2000  bbl.,  and  Apr. 
30,  3000  bbl.;  delivered  May  8,  1000  bbl.,  and  June  9, 4000  bbl. 
The  storage  charge  being  4J  ^  per  barrel  per  term  of  30  da. 
average  storage,  what  was  the  amount  of  the  bill  to  render  ? 

SOLUTION.     The  solution  of  this  problem  is  clearly  shown  in  the  following 
statement  of  account : 


STORAGE 


437 


ACCOUNT  OF  FLOUR  KECEIVED  AND  DELIVERED  BY 

EASTEKN   STORAGE   CO., 
For    A.    M.    BRIGGS    &    CO. 


DATE 

KECEIPTS 

DELIVERIES 

BALANCE 

TIME  IN 
STORAGE 

QUANTITY  IN 
STORAGE  FOR  1  DA. 

1907 

Apr. 

10 
30 

2000  bbl. 
3000  bbl. 

2000  bbl. 
5000  bbl. 

20  da. 
8  da. 

40000  bbl. 
40000  bbl. 

May 
June 

8 
9 

1000  bbl. 
4000  bbl. 

4000  bbl. 
0000  bbl. 

32  da. 
00  da. 

128000  bbl. 
00000  bbl. 

5000  bbl. 

5000  bbl. 

30)208000  bbl. 

Average  storage  for  1  mo.  =  6933|  bbl. 
69331  bbl.  at  4^  =  $  312,  the  amount  of  the  bill  to  render. 

WRITTEN  EXERCISE 

1.  The  Quincy  Storage  and  Warehouse   Co.    received  and 
delivered  on  account  of  Boynton  Travers  &  Co.  sundry  barrels 
of  apples  as  follows  :  received  Dec.  1,  1906,  1000  bbl.,  Dec.  26, 
2000   bbl.;    delivered   Feb.    1,  500   bbl.,   Mar.   1,   1000   bbl., 
Mar.  15,  1100  bbl.,  Mar.  31,  400  bbl.     If  the  charges  were 
6^  per  barrel  per  term  of  30  da.  average  storage,  what  was 
the  amount  of  the  bill  to  render? 

2.  The  Central  Storage  Warehouse  Co.  received  and  delivered 
on  account  of  A.  S.  Osborn  &  Co.  sundry  bushels  of  wheat  as 
follows  :   received  Oct.  1, 17,600  bu.,  Nov.  15,  3600  bu.,  Dec.  18, 
4200  bu.,  Dec.   27,  4320  bu.;    delivered  Oct.   31,  10,000  bu., 
Dec.  4,  10,720  bu.,  Dec.  19,  4000  bu.,  Dec.  28,  5000  bu.     If 
the  charges  were  1|  ^  per  bushel  per  term  of  30  da.  average 
storage,  what  was  the  amount  of  the  bill  to  render  ? 

3.  Metropolitan  Storage  Co.  received  and  delivered  on  ac- 
count of  Chas.  B.  Sherman  sundry  barrels  of  flour  as  follows : 
received  Nov.  15,  1906,  1800  bbl.,  Nov.  30,  1000  bbl.,  Dec.  18, 
600  bbl.,   Jan.   30,  3000  bbl.  ;    delivered   Dec.  1,    1000   bbl., 
Dec.  31,  1900  bbl.,  Jan.  31,  600  bbl.,  Feb.  5,  600  bbl.,  Apr.  30, 
2300  bbl.     If  the  charges  were  5J^  per  barrel  per  term  of  30 
da.  average  storage,  what  was  the  amount  of  the  bill  to  render  ? 


438  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN    REVIEW   EXERCISES 

1.  I  bought  wheat  at  $0.80  per  bushel.     Allowing  6%  for 
waste  and  incidentals  and  2  %  for  storage,  how  much  must  I 
receive  per  bushel  for  the  wheat  to  realize  a  gain  of  10.12 
per  bushel  ? 

2.  A  produce  dealer  bought  150  T.  cabbage  at  $  5.50  per  ton. 
He  paid  90  f  per  ton  for  storage  and  then  sold  the  cabbage  at  a 
clear  profit  of  25%.     How  much  did  he  receive  per  ton  and 
what  was  his  gain  ? 

3.  Nov.  1  a  speculator  bought  5000  bbl.  apples  at  $2.25  per 
barrel  and  put  them  in  storage.     Feb.   1  he  withdrew  them 
from  the  storage  warehouse.     He  had  them  sorted  and  repacked, 
when  he  found  that  he  had  only  4600  bbl.    of  sound  apples. 
These   he   sold   at   $3.50  per  barrel.    If  the    storage    charges 
were   5^  per  barrel  per  month  or  fraction  thereof,   and  the 
charges  for  repacking  were  $500,  did  he  gain  or  lose,  and  how 
much  ?  what  per  cent  ? 

4.  Dec.  15,  1906,  A.   L.   Farley  bought  1000  bbl.  flour  at 
$4  and  placed  it  with  the  Union  Warehouse  Co.  for  storage. 
Jan.  15  he  bought  3000  bbl.  flour  at  $4.15  and  placed  it  with 
the  same  warehouse  company  for  storage.     On  Feb.  15  he  with- 
drew 2000  bbl.  from  storage  and  sold  it  at  $5.85,  on  Mar.  25 
he  withdrew  1000  bbl.  and  sold  it  at  $  5.62^,  on  Apr.  1  he  with- 
drew 1000  bbl.  and  sold  it  at  $  5.87J.     If  the  storage  charges 
were  5^  per  barrel  per  month  or  fraction  thereof,  and  cartage 
and  incidentals  cost  $  100,  did  he  gain  or  lose,  and  how  much  ? 


APPENDIX 

TABLES    OF   MEASURES 

MEASURES  OF  CAPACITY 

Liquid  Measure  Dry  Measure 

4  gills     =  1  pint  2  pints    =  1  quart 

2  pints    =  1  quart  8  quarts  =  1  peck 

4  quarts  =  1  gallon  4  pecks  =  1  bushel 

=  2:31  cubic  inches  =2150.42  cubic  inches 

Barrels  and  hogsheads  vary  in  size  ;  but  in  estimating  the  capacity  of  tanks 
and  cisterns  31.5  gal.  are  considered  a  barrel,  and  2  bbl.,  or  63. gal.,  a  hogshead. 

A  heaped  bushel,  used  for  measuring  apples,  corn  in  the  ear,  etc.,  equals 
2747.71  cu.  in.  A  dry  quart  equals  67.2  cu.  in.,  and  a  liquid  quart  57.75 
cu.  in. 

MEASURES  OF   WEIGHT 

Avoirdupois  Weight  Troy  Weight 

16  ounces  =  1  pound  24  grains  =  1  pennyweight 

100  pounds  =  1  hundredweight  20  pennyweights  =  1  ounce 

2000  pounds  =  1  ton  12  ounces  =  1  pound 

Apothecaries'  Weight  Comparative  Weights 

20  grains     =  1  scruple  1  Ib.  troy  or  apothecaries'  =  5760  gr. 

3  scruples  —  1  dram  1  oz.  troy  or  apothecaries'  =    480  gr. 

8  drams     —  1  ounce  1  Ib.  avoirdupois  =  7000  gr. 

12  ounces    =  1  pound  1  oz.  avoirdupois  =  437^  gr. 

The  ton  of  2000  Ib.  is  sometimes  called  a  short  ton.  There  is  a  ton  of  2240  Ib. , 
called  a  long  ton,  used  in  all  customhouse  business  and  in  some  wholesale  trans- 
actions in  mining  products. 

In  weighing  diamonds,  pearls,  and  other  jewels,  the  unit  generally  employed 
is  the  carat,  equal  to  3.2  troy  grains.  The  term  "  carat"  is  also  used  to  express 
the  number  of  parts  in  24  that  are  pure  gold.  Thus,  gold  that  is  14  carats  fine 
is  ||  pure  gold  and  \%  alloy. 

Miscellaneous  Weights 

1  keg  of  nails       =  100  pounds  1  barrel  of  salt  =  280  pounds 

1  cental  of  grain  =  100  pounds  1  barrel  of  flour  =196  pounds 

1  quintal  of  fish  =  100  pounds  1  barrel  of  pork  or  beef  =  200  pounds 

A  cubic  foot  of  water  contains  6£  gal.  and  weighs  62£  Ib.,  avoirdupois. 

439 


440 


PRACTICAL   BUSINESS   AEITHMETIC 


MEASURES  OF  EXTENSION 


Long  Measure 


12  inches  =  1  foot 

3  feet  =  1  yard 

5^  yards,  or  16  £  feet  =  1  rod 
320  rods,  or  5280  feet  =  1  mile 


Surveyors'  Long  Measure 

7.92  inches  =  1  link 

25  links  =  1  rod 

4  rods,  or  100  links  =  1  chain 
80  chains  =  1  mile 


City  lots  are  usually  measured  by  feet  and  decimal  fractions  of  a  foot ;  farms, 
by  rods  or  chains. 


Miscellaneous  Long  Measures 

4  inches  =1  hand 

6  feet  =  1  fathom 

120  fathoms          =  1  cable  length 
1.15  miles,  nearly,  =  1  knot,  or 
1  nautical  or  geographical  mile 


Square  Measure 

144  square  inches  =  1  square  foot 
9  square  feet      =  1  square  yard 
30J  square  yards  =  1  square  rod 
160  square  rods      =  1  acre 
640  acres  =  1  mile 


The  hand  is  used  in  measuring  the  height  of  horses  at  the  shoulder.  The 
fathom  and  cable  length  are  used  by  sailors  for  measuring  depths  at  sea.  The 
knot  is  used  by  sailors  in  measuring  distances  at  sea.  Three  knots  are  frequently 
called  a  league. 


Surveyors'  Square  Measure 


Cubic  Measure 


625  square  links  =  1  square  rod  1728  cubic  inches  =  1  cubic  foot 
10  square  rods  —  1  square  chain  27  cubic  feet  =  1  cubic  yard 
10  square  chains  =  1  acre 

640  acres  =  1  square  mile 

36  square  miles   =  1  township 


128  cubic  feet      =  1  cord 

1  cubic  yard    =  1  load  (of  earth,  etc.) 
24|  cubic  feet     =  1  perch 


The  square  rod  is  sometimes  called  a  perch.  The  word  rood  is  sometimes 
used  to  mean  40  sq.  rd.  or  |  A.  In  the  government  surveys,  1  sq.  mi.  is  called 
a  section. 

The  perch  of  stone  or  masonry  varies  in  different  parts  of  the  country  ;  but 
it  is  usually  considered  as  1  rd.  long,  1  ft.  high,  and  1£  ft.  thick,  or  24|  cu.  ft. 


Angular  Measure 


60  seconds  =  1  minute 
60  minutes  =  1  degree 


90  degrees  =  1  right  angle 
360  degrees  =  1  circumference 


Angular  (also  called  circular)  measure  is  used  principally  in  surveying,  navi- 
gation, and  geography  for  measuring  arcs  of  angles,  for  reckoning  latitude  and 
longitude,  for  determining  locations  of  places  and  vessels,  and  for  computing 
difference  of  time. 

A  minute  of  the  earth's  circumference  is  equal  to  a  geographical  mile.  A 
degree  of  the  earth's  circumference  at  the  equator  is  therefore  equal  to  about 
69  statute  miles. 


TABLES  OF   MEASURES  441 

MEASURES  OF  TIME 

60  seconds  =  1  minute  12  months  =  1  year 

60  minutes  =  1  hour  360  days       =  1  commercial  year 

24  hours      =  1  day  365  days       =  1  common  year 

7    days        =  1  week  366  days       =  1  leap  year 

30  days        =  1  commercial  month  100  years      =  1  century 

September,  April,  June,  and  November  have  30  da.  each  ;  all  of  the  other 
months  have  31  da.  each,  except  February,  which  has  28  da.  in  a  common  year 
and  29  da.  in  a  leap  year. 

Centennial  years  that  are  divisible  by  400  and  other  years  that  are  divisible 
by  4  are  leap  years. 

In  running  trains  across  such  a  broad  stretch  of  country  as  the  United  States, 
it  is  highly  important  to  have  a  uniform  time  over  considerable  territory.  Rec- 
ognizing this,  in  1883,  the  railroad  companies  of  the  United  States  and  Canada 
adopted  for  their  own  convenience  a  system  of  standard  time.  This  system 
divides  the  United  States  into  four  time  belts,  each  covering  approximately  15° 
of  longitude,  7^°  of  which  are  east  and  7|c  west  of  the  governing  meridian.  The 
region  of  eastern  time  lies  approximately  7|°  each  side  of  the  75th  meridian, 
and  the  time  throughout  this  belt  is  the  same  as  the  local  time  of  the  75th  merid- 
ian. Similarly,  the  regions  of  central,  mountain,  and  Pacific  time  lie  approxi- 
mately 7|°  each  side  of  the  90th,  105th,  and  120th  meridians,  respectively,  and 
the  time  throughout  each  belt  is  determined  by  the  local  time  of  the  governing 
meridian  of  that  belt.  There  is  just  one  hour's  difference  between  adjacent  time 
belts.  Thus,  when  it  is  11  o'clock  A.M.  by  eastern  time,  it  is  10  o'clock  A.M.  by 
central  time,  9  o'clock  A.M.  by  mountain  time,  and  8  o'clock  A.M.  by  Pacific  time. 
Since  railroad  companies  change  the  time  at  important  stations  and  termini, 
regardless  of  the  longitude  of  such  stations  and  termini,  the  boundaries  of  the 
time  belts  are  quite  irregular. 

MEASURES  OF  VALUE 

United  States  Money  English  Money 

10  mills     =  1  cent  4  farthings  =  1  penny 

10  cents     =  1  dime  12  pence       =  1  shilling 

10  dimes    =  1  dollar  20  shillings  =  1  pound  sterling 

10  dollars  =  1  eagle  =  $4.8665 

The  term  "  eagle  "  is  seldom  used  in  business.  The  mill  is  not  a  coin,  but  the 
name  is  frequently  used  in  some  calculations.  In  Canada  the  units  of  money 
are  the  same  as  in  the  United  States.  1  far.  =  f|^  ;  Id.  =  2-fop  ;  Is.  = 


French  Money  German  Money 

100  centimes  =  1  franc  =  $0.193  100  pfennigs  =  1  mark  =  $0.238 

MISCELLANEOUS  MEASURES 

Counting  by  12  Counting  Sheets  of  Paper 

12  things  =  1  dozen  24  sheets  =  1  quire 

12  dozen    =  1  gross  20  quires  =  1  ream 

12  gross    =  1  great  gross  =  480  sheets 


442 


PRACTICAL   BUSINESS   ARITHMETIC 


BUSINESS   ABBREVIATIONS 


A  .    . 

.  acre 

Mar.  .     . 

Apr.  . 

.  April 

mdse. 

Aug.  . 

.  August 

Messrs.    . 

bbl.    . 

.  barrel  ;  barrels 

bdl.    . 

.  bundle;  bundles 

mi. 

. 

bg.     . 
bkt.    . 

.  bag;  bags 
.  basket;  baskets 

min.  .     . 
mo.     .     . 

bl.      . 

.  bale;  bales 

Mr.     .     . 

. 

bu.     . 

.  bushel;  bushels 

Mrs.   .     . 

. 

bx.     . 

.  box  ;  boxes 

N.       .     . 

cd.      . 

.  cord;  cords 

No.     .     . 

. 

ch.      . 

.  chain  ;  chains 

Nov.  .     . 

c.i.f.    . 

.  carriage  and  insurance  free 

Oct.    .     . 

. 

Co.     . 

.  company;  county 

oz. 

. 

c.o.d.  . 

.  collect  on  delivery 

p.  ... 

. 

coll.    . 

.  collection 

pc.      .     . 

Cr.      . 

.  creditor;  credit 

per.     .     . 

. 

cs. 

.  case  ;  cases 

per  cent. 

ct. 

.  cent  ;  cents  ;  centime 

cu.  ft. 

.  cubic  foot  ;  cubic  feet 

pk.      .     . 

. 

cu.  in. 

.  cubic  inch  ;  cubic  inches 

pkg.    .     . 

. 

cu.  yd. 

.  cubic  yard  ;  cubic  yards 

pp.      .     . 

. 

cwt.    . 

.  hundredweight 

pr.       .     . 

. 

d.  .     . 

.  pence 

pt.       .     . 

. 

da.      . 

.  day;  days 

pwt.    .     . 

Dec.    . 

.  December 

doz.     . 

.  dozen;  dozens 

qr.       .     . 

. 

Dr.      . 

.  debtor  ;  debit  ;  doctor 

qt.       .     . 

. 

E.  .     . 

.  east 

rd.       .     . 

§ 

ea. 

.  each 

rrn.     .     . 

e.g.     . 

.  exempli    gratia,      for    ex- 

Rm.(or M. 

) 

ample 

s.    .     .     . 

etc.     . 

.  el  ccetera,  and  so  forth 

S.  .     .     . 

far.     . 

.  farthing  ;  farthings 

sec.     .     . 

. 

Feb.   . 

.  February 

sq.  ch. 

, 

f.o.b.  . 

.  free  on  board 

fr.        . 

.  franc  ;  francs 

sq.  ft.      . 

. 

ft.        . 

.  foot;  feet 

sq.  mi.     . 

. 

gal.     . 

.  gallon;  gallons 

.  gill;  gills 

sq.  rd.      . 

gr-       • 

.  grain  ;  grains 

sq.  yd.     . 

. 

gro.     . 

.  gross 

hhd.    . 

.  hogshead;  hogsheads 

T.  .    .     . 

hf.  cht. 

.  half  chest  ;  half  chests 

tb.       .     . 

hr.      . 

.  hour;  hours 

Tp.     .     . 

i.e. 

.  id  est,  that  is 

viz.     .     . 

, 

in. 

.  inch;   inches 

via      .     . 

. 

Jan.    . 

.  January 

wk.     .     . 

kg.      . 

.  keg;  kegs 

wt. 

, 

1.    .     . 

.  link  ;  links 

yd.      .     . 

Ib.       . 

.  pound;  pounds 

yr.       .     . 

. 

.  March 

merchandise 

.  Messieurs,    Gentlemen  ; 
Sirs 

mile;  miles 

minute;  minutes 

month ;  months 

Mister 

Mistress 

north 

number 

November 

October 

ounce;  ounces 

page 

piece ;  pieces 
.  by  the ;  by 
.  per  centum,  by  the  hun- 
dred 

.  peck ;  pecks 
.  package ;  packages 

pages 

pair;  pairs 
.  pint;  pints 
.  pennyweight;      penny- 
weights 
.  quire;  quires 
.  quart;  quarts 
.  rod  ;  rods 

ream  ;  reams 

Reichsmark,  Mark 

shilling;  shillings 
.  South 

.  second ;  seconds 
.  square     chain;     square 

chains 

.  square  foot ;  square  feet 
.  square      mile;      square 

miles 

.  square  rod ;  square  rods 
.  square     yard;      square 
yards 

ton 

.  tub ;  tubs 
.  township;  townships 

videlicet,  namely ;  to  wit 
.  by  way  of 
.  week ;  weeks 
.  weight;  weigh 
.  yard;  yards 

year;  years 


BUSINESS   SYMBOLS  AND  ABBREVIATIONS      443 


a/e     account 
«/«      account  sales 
4-        addition 
(  )>~  aggregation 
&         and 

and  so  on 

@         at;  to 
c/0       care  of 
?          cent;  cents 
v/        check  mark 

degree 

-r-         division 
$          dollar;  dollars 


BUSINESS   SYMBOLS 

=     equal ;  equals 
'       foot;  feet; 
minutes 
C     hundred 

inch  ;  inches ;  seconds 
x     multiplication 
#     number,  if  written 
before  a  figure; 
pounds,  if  written 
after  a  figure 

11  one  and  one  fourth 

12  one  and  two  fourths  ; 

one  and  one  half 


I8     one  and  three 

fourths 
^P     per;  by 
%      per  cent ; 

hundredth ; 
hundredths 
£      pounds  sterling 

since 
—     subtraction 

therefore 
M     thousand 
Ye    5  shillings  6  pence  ; 
five  sixths 


INDEX 


Abbreviations,  442. 

Above  par,  390. 

Abstract  number,  50. 

Account,  41. 

Account  current,  405,  407. 

Account  purchase,  267,  271. 

Account  sales,  267,  384. 

Acute  angle,  193. 

Acute-angled  triangle,  194. 

Adding  machine,  197. 

Addition,  10,  88,  119,  184. 

Ad  valorem  duty,  285,  289. 

Agent,  266. 

Aliquot  parts,  150. 

Altitude,  196. 

Amount,  228,  322. 

Angle,  193. 

Angular  measure,  440. 

Apothecaries'  weight,  439. 

Approximations,  140. 

Arabic  numerals,  2. 

Arc,  194. 

Areas,  196. 

Assessment,  389,  392. 

At  a  discount,  358,  390. 

At  a  premium,  358,  390. 

At  par,  358. 

Average,  79. 

Average  clause,  278. 

Average  date  of  payment,  377. 

Average  investment,  428. 

Average  storage,  436. 

Average  term  of  credit,  377. 

Avoirdupois  weight,  439. 

Bank  discount,  320,  321. 

Bank  drafts,  350,  352. 

Bank  loans,  328. 

Bank  money  order,  347. 

Bankers'  bills  of  exchange,  367,  369. 

Bankers'  daily  balances,  340. 

Banker's  sixty -day  method  of  interest, 

297. 

Banking,  294. 
Base,  196,  228,  232. 
Base  line,  199. 


Bear,  406. 

Below  par,  390. 

Bill  of  lading,  358. 

Bills,  39,  40,  59,  63,  100,  101,  128,  147, 
157,  158,  160,  161,  162,  163, 164,  165, 
166,  174, 179, 189,  192,  218,  244,  249, 
250,  251,  259,  264,  265,  291,  292. 

Bills  and  accounts,  160. 

Bills  of  exchange,  367,  369,  370,  371. 

Bins,  222. 

Blank  indorsement,  309. 

Board  foot,  215. 

Bonds,  397,  398. 

Brick  work,  220. 

Broker,  266. 

Brokerage,  266,  391. 

Bull,  406. 

Bullion,  9. 

Buying  bonds,  400. 

Buying  by  the  hundred,  99. 

Buying  by  the  thousand,  99. 

Buying  by  the  ton,  102. 

Buying  on  commission,  270. 

Buying  stocks,  394. 

Calculation  tables,  224. 

Cancellation,  109. 

Capacity,  221. 

Capital,  419. 

Capital  stock,  388. 

Carpeting,  209. 

Cash  account,  41. 

Cash  balance,  385. 

Cashier's  check,  353. 

Certificate  of  deposit,  353. 

Change  memorandum,  172. 

Charter,  388. 

Checking  results,  20,  32,  52,  57,  58,  67, 

81,  82,  83. 
Checks,  5,  20,  32,  52,  57,  58,  67,  350, 

354,  375,  392. 
Circle,  194. 
Circumference,  194. 
Cisterns,  223. 
Clearing  house,  350,  351. 
Code,  348. 


445 


446 


INDEX 


Co-insurance,  274. 

Collateral  note,  330. 

Collection  and  exchange,  326,  356. 

Commercial  bank,  320,  340. 

Commercial  bills  of  exchange,  367,  370, 

371. 

Commercial  discounts,  242. 
Commercial  drafts,  321,  356. 
Commission,  266. 
Commission  merchant,  266. 
Common  accounts,  41. 
Common  denominator,  118. 
Common  divisor,  110. 
Common  fractions,  113. 
Common  stock,  390. 
Comparative  weights,  439. 
Composite  number,  107. 
Compound  accounts,  380. 
Compound  interest,  314,  343. 
Concrete  number,  50. 
Consecutive  numbers,  18. 
Consignee,  266. 
Consignment,  267. 
Consignor,  266. 
Conversion  of  fractions,  139. 
C  ,-d,  215. 
Corporation,  388. 
Corporation  tax,  283. 
Counting  by  12,  441. 
Counting  sheets  of  paper,  441. 
Coupon  bond,  398. 
Credit,  41. 
Cube,  213. 
Cubic  measure,  440. 
Customhouse,  285. 
Customs  duties,  285. 
Cylinder,  219. 

Day  method  of  interest,  295. 
Days  of  grace,  321. 
Debit,  41. 
Decimal,  85. 
Decimal  fractions,  85. 
Decimal  system,  3. 
Decimal  units,  85. 
Demand  note,  309,  329. 
Denominate  quantities,  181. 
Denominator,  113. 
Deposit  slip,  355. 
Depositors'  ledger,  38. 
Diameter,  194. 
Difference,  328. 
Discount  series,  242,  245. 
Distances,  193. 
Dividend,  64,  389,  392,  411. 


Division,  64,  69,  95,  98,  133,  187. 

Divisor,  64. 

Divisors,  110. 

Documentary  bill   of  exchange,   367, 

371. 

Domestic  exchange,  346. 
Drafts,  320,  321,  328,  356,  360. 
Drawee,  321. 
Drawer,  321. 
Dry  measure,  439. 
Duties,  285. 

Endowment  policy,  410,  413,  414. 
English  money,  441. 
Equated  date,  377. 
Equation  of  accounts,  376. 
Equilateral  triangle,  194. 
Even  number,  107. 
Exact  interest,  311. 
Exchange,  346,  353. 
Exchange  quotations,  368. 
Expense  account,  43. 
Exponent,  50. 

Express  money  order,  347,  366. 
Expressage,  178. 
Extended  insurance,  411. 

Face,  309. 

Factor,  50,  107. 

Factoring,  108. 

Final  results,  117. 

Finding  the  base,  232. 

Finding  the  cost,  255. 

Finding  the  difference  between  dates, 

185. 

Finding  the  gain  or  loss,  253. 
Finding  the  percentage,  228. 
Finding  the  per  cent  of  gain  or  loss,  254. 
Finding  the  rate,  230. 
Fire  insurance,  273. 
Firm  note,  326. 
First-mortgage  bonds,  397. 
Five-eighths  pitch,  205. 
Flooring,  208. 

Fluctuation  of  rates  of  exchange,  358. 
Focal  date,  377. 
Foreign  money,  362. 
Foreign  money  orders,  366. 
Fractional  relations,  136. 
Fractions,  85. 
Free  list,  285. 
Freight  bill,  179. 
Freightage,  178. 
French  money,  441. 
Full  indorsement,  309. 


INDEX 


447 


Gain,  41. 

Gain  and  loss,  252. 

Gas  meters,  101. 

German  money,  441. 

Government  bonds,  398. 

Graphic  representations,  138,  239,  241. 

Greatest  common  divisor,  110. 

Gross  price,  243. 

Gross  weight,  38. 

Grouping,  11,  14. 

Guaranty,  266. 

Heaped  bushel,  221. 
Holder,  320. 
Horizontal  addition,  24. 
Hypotenuse,  202. 
Hypothecating,  406. 

Important  per  cents,  228. 
Improper  fraction,  114. 
Incomes  and  investments,  402. 
Indorsements,  309,  336. 
Inheritance  tax,  283. 
Insurance,  273. 
Insurance  rates,  410. 
Insurer,  274. 
Interest,  294. 
Interest  days,  343. 
Interest  term,  343. 
Interest-bearing  note,  309. 
International    postal    money    orders, 

366. 

Invoice,  150. 
Inward  foreign  entry,  293. 

Joint  and  several  note,  310,  326. 
Joint  note,  310,  326. 

Key,  260. 

Kinds  of  life  insurance  policies,  410. 

Lateral  surface,  219. 

Least  common  denominator,  118. 

Least  common  multiple,  112. 

Letter  of  advice,  268,  361. 

Letter  of  credit,  372. 

Letter  ordering  goods,  175. 

Liability,  41. 

License  fee,  280. 

Life  insurance,  410. 

Life  insurance  companies,  410. 

Like  numbers,  7. 

Limited  life  policy,  410. 

Liquid  measure,  339. 

Listing  goods  for  catalogues,  263. 


Long  measure,  440. 
Loss,  41. 
Lumber,  215. 

Maker,  309. 

Making  change,  33. 

Manifest,  286. 

Margins,  405,  408. 

Marine  insurance,  278. 

Market  value,  390. 

Marking  goods,  260. 

Masonry,  220. 

Maturity,  320. 

Maturity  table,  322. 

Measures  of  capacity,  439. 

Measures  of  extension,  440. 

Measures  of  time,  441. 

Measures  of  value,  441. 

Measures  of  weight,  439. 

Merchandise  account,  442. 

Merchants'    method    of    partial   pav- 

ments,  337. 
Metric  system,  363. 
Mint  par  of  exchange,  367. 
Miscellaneous  measures,  440,  441. 
Miscellaneous  weights,  439. 
Mixed  numbers,  114. 
Model  figures,  19,  21,  22,  23. 
Money  orders,  346. 
Mortgage  note,  335. 
Multiple,  50. 
Multiplication,  50,  55,  57,  59,  60,  61, 

92,  127,  132,  187. 
Multiplying  machine,  55. 
Municipal  bonds,  398. 
Mutual  insurance  company,  274. 

Negotiable,  309. 

Net  capital,  41. 

Net  gain,  41. 

Net  insolvency,  41. 

Net  loss,  41. 

Net  price,  243. 

Net  weight,  39. 

Notation,  2,  86. 

Notes,  9,  308,  310,  330,  335. 

Numeration,  2,  86. 

Numeration  table,  4,  86. 

Numerator,  113. 

Obtuse  angle,  193. 
Obtuse-angled  triangle,  194. 
Odd  number,  197. 
One-fourth  pitch,  204. 
One-half  pitch,  204. 


448 


INDEX 


Open  policy,  274. 
Orders  of  units,  3. 
Ordinary  life  policy,  410. 

Paid-up  policy,  411. 

Painting,  207. 

Papering,  211. 

Par  value,  390. 

Parenthesis,  31. 

Partial  payments,  322. 

Partitive  proportion,  416. 

Partners,  419. 

Partnership,  417. 

Pay    rolls,    80,    172,    173,    176,    177, 

226. 

Pay-roll  memorandum,  173. 
Payee,  309,  321. 
Per  cent,  86,  227. 
Per  cents  of  decrease,  235. 
Per  cents  of  increase,  234. 
Percentage,  227. 
Perch,  220. 
Perimeter,  194. 
Periodic  interest,  313. 
Periods,  4. 

Perpendicular  lines,  193. 
Personal  accounts,  42. 
Pitch  of  roof,  204. 
Place  value,  3. 
Plane  surface,  193. 
Plastering,  206. 
Policy,  274. 
Poll  tax,  280. 
Port  of  delivery,  285. 
Port  of  entry,  285. 
Postal  information,  72. 
Postal  money  order,  346. 
Power,  51. 

Practical  measurements,  193. 
Preferred  stock,  389. 
Premium,  274. 
Present  worth,  41. 
Prime  number,  107. 
Principal,  266,  294. 
Principal  meridian,  199. 
Problems  in  interest,  312. 
Proceeds,  322. 
Promissory  notes,  9,  308,  310,  335,  329, 

330. 

Properties  of  9,  81. 
Properties  of  11,  82. 
Property  insurance,  273. 
Property  tax,  280. 
Proprietary  account,  243. 
Public  lands,  199. 


Qualified  indorsement,  309. 
Quotient,  64. 

Radical  sign,  200. 

Radius,  194. 

Ranges,  199. 

Rate,  228,  294. 

Rate  of  exchange,  347,  352,  358,  368. 

Reading  decimals,  86. 

Rectangle,  193. 

Rectangular  solids,  213. 

Reduction,  115,  116,  117, 118,  182,  183. 

Reference  method  of  interest,  307. 

Registered  bond,  399. 

Remainder,  64. 

Repeaters,  260. 

Reserve,  411. 

Resource,  41. 

Review  of  the  common  tables,  181. 

Right  angle,  193. 

Right-angled  triangle,  194.    . 

Roman  numerals,  6. 

Roofing,  203. 

Savings  bank,  343. 

Savings-bank  accounts,  343. 

Scalene  triangle,  194. 

Second-mortgage  bonds,  397. 

Section,  199. 

Selling  by  the  hundred,  99. 

Selling  by  the  thousand,  99. 

Selling  by  the  ton,  102. 

Selling  on  commission,  268. 

Separatrix,  3. 

Share,  388. 

Shipment,  267. 

Shipping  invoice,  269. 

Short  methods,  55,  69,  120,  130. 

Sight  draft,  356. 

Similar  fractions,  118. 

Simple  accounts,  377. 

Simple  interest,  295. 

Simple  storage,  433. 

Sinking  fund,  317. 

Six  per  cent  method  of  interest,  305. 

Sixteen  to  one,  130. 

Solids,  213. 

Solution  of  problems,  142. 

Specific  duty,  285. 

Square,  193,  203. 

Square  measure,  440. 

Square  root,  200. 

Standard  time,  441. 

State  bonds,  398. 

Statements,  45,  46,  170,  171,  258,  339. 


INDEX 


449 


Statutory  weights  of  the  bushel,  190. 

Stock  broker,  391. 

Stock  certificates,  388,  389,  390. 

Stock  company,  388. 

Stock  exchanges,  404. 

Stock  insurance  company,  274. 

Stockholder,  388. 

Stocks  and  bonds,  388. 

Stone  work,  220. 

Storage,  443. 

Stricken  bushel,  221. 

Subtraction,  31,  90,  124,  184. 

Surface,  193. 

Surplus,  411. 

Surveyors'  long  measure,  440. 

Surveyors'  square  measure,  440. 

Table  of  aliquot  parts,  152. 
Table  of  bond  quotations,  400. 
Table  of  common  measures,  439. 
Table     ol    compound     interest,    315, 

317. 

Table  of  foreign  coins,  287. 
Table  of  important  per  cents,  228. 
Table  of  insurance  rates,  276*  411. 
Table  of  simple  interest,  308. 
Table  of  stock  quotations,  394. 
Table  of  time,  324. 
Table  of  twelfths,  262. 
Tables  of  metric  measures,  363. 
Tare,  38. 
Tariff,  285. 
Tax  rate,  281. 
Tax  table,  284. 
Taxes,  280. 


Telegrams,  176,  348. 

Telegraphic  money  order,  348. 

Telegraphic  rates,  349. 

Term  of  discount,  322. 

Term  of  storage,  433. 

Term  policy,  410. 

Terms  of  a  fraction,  114. 

Tests  of  divisibility,  108. 

Third-mortgage  bonds,  397. 

Time  note,  309. 

Time  sheets,  76,  77,  78,  80,  149,  172, 

173,  176,  177,  226. 
Time  slip,  177. 
Township,  199. 
Trade  discount,  242. 
Traveler's  check,  373,  374. 
Triangle,  194. 
Troy  weight,  439. 

Underwriter,  274. 
Unit,  7. 

Unit  fraction,  115. 
United  States  coins,  8. 
United  States  method  of  partial  pay- 
ment, 332. 
United  States  money,  8,  9,  441. 

Valued  policy,  274. 

Values  of  foreign  coins,  287. 

Vinculum,  31. 

Warehousing,  287. 
Weigh  tickets,  102,  106. 
Wood,  215. 


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